Leaving basement forms on permanently

What's not standard practice is for a wall to be poured so near another parallel foundation. That's a somewhat unique situation to begin with. Normally the floor system for an addition would rest on the original foundation unless there was a problem with the original. (I've since learned that the existing is a slab foundation. Obviously the new wall is necessary for the addition's basement.)

That said, this probably isn't a problem. The wood will eventually decay and cause some degree of soil settling, but you'd probably have than anyway. If you expect it and plan for it you should be fine.

One possible concern would be regarding waterproofing. If you're having the concreted sprayed, or if a membrane is being installed, you'll have to decide whether it'll be effective over the wood.

Otherwise it's really no different than tree roots or other organic material in the soil.

Sounds like a hack-job approach to me.

That wall could be built from concrete blocks (aka CMUs or concrete masonry units), with bond-block rows and reinforcing steel, and grouted full, making it effectively solid, without abandoning forms in place - or rather, the forms would be the block wall.

Of course, poured concrete contractors and masons are not usually the same people, so this would not be a solution a concrete contractor would be liable to think of.

Alternatively, a form never intended to be removed and not made of wood that will rot - the insulated concrete form or ICF. Two sheets of styrofoam tied together.

But your pictures imply that this is a done deal.

If termites are a problem in your area, they may find that form tasty.

Check with a termite control company and/or the state agency that studies termite control. Also check with your homeowner's insurance company. Having all that buried wood would invite termites.

It is possible to remove those forms. We did plenty of that when I worked for my dad. Usually contractors want to keep and re-use the form panels because they are expensive. There are only two real drawbacks to leaving the panels on the foundation:

1. You will not be able to coat the exterior of the foundation wall with any waterproofing. Usually something like an asphalt emulsion is used to prevent water ingress through the wall.
2. You might have a slight smell of diesel around the base of the structure since that is what is commonly used to spray on the panels to prevent the concrete from sticking to it.