Do studs in wooden buildings eventually get replaced as they lose their structural capacity?

No.

Wood frame construction is generally done for rigidity not strength. You can climb a tree and have the branches deflect significantly before they break - the strength is fine - if you build a house with just strength in mind then you'd be bouncing all over the place. Wood frame construction is instead designed for rigidity such that when you walk across the floor your book case isn't bouncing up and down.

You also have to take into account that a lot of walls are not strictly part of the structure. A lot of interior walls are only there to delineate spaces.

Now getting into the drilling a million holes over the years into studs such that they eventually fail. Studs are under compression but are very strong in compression. Rules for how you can notch or drill studs typically allow quite large holes for water pipes and waste water pipes.

"Holes in bearing wall studs may not exceed 40 percent of the width of the stud. Holes in non-bearing walls can’t exceed 60 percent of their width."

https://www.familyhandyman.com/project/drilling-holes-notching-and-boring-holes-in-wood-studs

Now given you can drill a hole 40% the width of the stud in a bearing wall, 40% of 3.5" width = 1.4" (~1 3/8). How many 1/8" holes does it take to equal 1 3/8" = 11 just to form the diameter of the allowable hole. I am not going to do the math on how many it would take to equal the full hole. These holes would all have to be in the same area to achieve the accepted weakening of this member. Now factor in that the full strength of the wall assembly at the weakened state is likely only required under 100 year design event conditions and like most things dictated by code we reach a factor of over engineering which should ensure safety and there should be no way you could drill enough holes in the lifetime of a building to put the structural integrity at risk.

A plumber or electrician drilling willy nilly through load bearing members is a different story - even then you likely only encounter problems at design conditions.

Yes there is a time when wood frame buildings have that happen it is a narrow case but I'll explain it. Back "in the day" cantilevered decks were all the rage for houses. These work by building the house so that the floor joists extend outside the house (generally 4 feet) with a deck built on them. So the effect you get is this deck just "floating" on the side of the house with no support at all. Often the joists were heavy thick 4 x 8s and such (even a 4 foot cantilevered deck can exert -significant- prying effect on the structure) I guess people thought that was a "totally cool look" (people think a lot of stupid construction designs are "totally cool look" unfortunately.)

The problem is that these are regular standard construction grade joists not treated wood. And over time the rain comes down and gets into the deck and rots the crap out of the joist. That rot then extends inward along the beam into the house itself. If it's let go long enough it can damage the house.

I can drive around neighborhoods out where our vacation house is and see deck after deck where it is apparent this has happened. The "fix" is to take a big nasty fugly saw (chainsaws often used) to cut the deck off the side of the house. Then they try to do what they can to calk and seal up the joist ends, and then put a facing board (treated lumber of course) on them and lag bolt that to the beam ends then construct a new deck on that, the end of deck now being supported by posts. It is particularly apparent with second floor decks because you have these ridiculous spindly 10-15 foot "legs" extending from the ground up to the second floor deck.

Then after driving around looking at that I come back to my own house, sit back and relax on my deck - and look up to my second floor deck and wish once more I could have 5 minutes with the builder to slap him silly for that idiocy. Then I wonder how much a big fugly saw will cost and if I can get another year out of it before having to buy one.

The only case of having to replace studs and such I’m aware of is from termite/dry rot damage. A number of years ago, my 2-story California home was to be painted. Before starting, the contractor went to repair some siding panels were edges were coming lose. He peeked behind one and went “oh, crap”. He had found severe termite damage. A bunch of studs has been reduced to not much more than the grain.

We had to have an engineer design a bracing system to support the upper floor while the siding was removed and the studs replaced. Our paint job turned into an expensive repair job. I can just imagine what could have happened if it hadn’t been found.

Buildings need to be maintained. Continuously. Part of that upkeep and repair involves replacing framing members. I've replaced wall studs because termites had run rampant for years. The repair involved constructing temporary walls inside the room to support the roof above while the studs were removed. When a tree falls on a roof rafters need to be replaced etc.

A structure can become so decrepit and run-down from lack of repair and abuse that it makes more sense financially to demolish it and start anew. But this is a subjective decision and depends on the predilections of the owner/buyer (ie a 17th century farm house may be quaint and worth the added effort to save).

As you stated "nothing lasts forever", but with care and diligence most of our homes can be around for generations before they reach a terminal state of disrepair.

Redundancy in wood framing significantly adds to its resilience. Though not all holes drilled into walls land on studs and the interior cladding, like sheetrock, is surprisingly strong. That cladding adds to the wall's strength.When a wall is damaged, there are a number of remedies that don't involve replacement of the stud. They include:

The practice of "sistering" joists or studs when an existing structural member loses its ability to maintain rigidity by itself. Sistering involves fastening a new structural member to an existing member.

Notching and blocking is another common technique that can be done to a damaged area, often seen in plumbing applications when it would be impractical to drill a hole and pass a pipe. There are special circumstances where notching and blocking are allowed depending on the situation. A notch can be cut out and have a block installed tightly on portions of objects under compression. It is not uncommon to see notching and blocking paired with sistering, bracing, or blocking to other existing structural members as described below.

Bracing is another repair technique which will involve sandwiching a compromised structural member between two other like structural members, or by using blocking between the compromised structural member and another structural member. Bracing can be done on objects experiencing compression or tension. Bracing is common in prefabricated roof design and also in deck construction and floor truss systems.

There is laminating which is similar to bracing or sistering but involves building up layers. It is often done to prefabricated truss systems that have received modification or repair where pieces of structural plywood are fastened to either side of a joint on a truss. Adding cladding to the side of a house is a form of laminating as the outside cladding, usually known as "sheathing", and inside cladding like sheetrock, make up layers of a wall adding to it's rigidity.

Binding or strapping can be used for repair. It involves wrapping a rope, wire, or cable around a splintered component, or can be used as a method of attachment when bracing or sistering. Strapping is often used when tying large beams together such as in log cabin homes, or fence posts. It is very common in prefabricated roof trusses, and diagonally on walls needing stiffening or lacking rigidity.

Adhesives added to splintered framing members is another repair. It is usually done with a mechanical method above, however it can be used by itself in some situations.

More care must be taken in load baring components than just partitioning components. Modern residential framing often involves using boards that are spliced (tenon cut and glued) together in non-load baring applications such as in partition walls where resistance to shear forces and horizontal deflection is not structurally significant.

In 15 years as a framing and remodeling carpenter I've only replaced a couple of studs due to fastener damage in residential situations that had television mounts improperly installed. Most structural repairs I've done have been due to water damage over time followed by animal action. The latter usually leading to water damage. Insects do do damage in Minnesota where I live but usually are present after water damage has occurred, or rodent activity was present. I have done a couple of repairs to fire damaged structures, and one vehicle building collision.

A dock truck needing a 14' high door drove through a 12' high door taking the header and header support posts (3 studs laminated together) with it on the gable end of the building. Despite a 14' high by 12'9" hole made, there was no detectable damage to the gable truss, roof, or surrounding framing. This was in Minnesota in the winter and there was easily a foot of sitting snow on the roof. It even ripped a copper natural gas line that was attached to the header without breaking it even though the gas line was holding a good amount of the header weight!