Why did the old-school thermal flashers remain in use for so long?

At the time your mg was originally made, the thermal flasher unit was cheap and effective. The use of electronics in most cars came along later, such as electronic ignition only became common place in cars in the 80's and those were with ballast resistors which was a common fail point.

And as for wasting energy - well they may do, but it is a fraction of the energy wasted in turning fuel into motion...

In comparison with a flasher built with a few semi-conductors: They're bigger in size,

No, not really. Electronics were pretty big until recently. In 70's a transistor that could hold enough current for a blinker alone was bigger than the entire flasher, not even talking about cost.

and probably more expensive, considering their relatively complex and precise mechanical construction.

But you forget about capital costs. The factories building thermal flashers were already up and running. Even if electronic flasher is £2 cheaper, how many do you have to install to cover the cost of setting up new supply?

more prone to failure

A car is a very bad environment for electronics. It can become very hot (every 10 degrees cuts lifetime of electronics in half), very cold (most semiconductors are not rated for operation below -20), the electrical grid is unstable (11-14 volts is typical range - just typical because values outside it WILL happen) and the noise from ignition system is horrible.

Plus, you haven't specified what "more prone to failure" means. If, let's say, the thermal flasher failure rate is 100% in 10 years and electronics is 30% in same timeframe, it still doesn't paint the whole picture. Flashers continuously wear down, so they can simply be engineered to withstand about 5 years, and most units fail after that. But - who cares, the warranty period is over. Electronics, on the other hand, don't wear down gradually, let's say it just has a random chance by being killed by voltage spike from the starter. So even if flashers are overall less reliable, they won't show up in warranty claims while electronics will. Also, things breaking down in an old car are simply expected, but in a new car - that's very bad press.

The movement from flashers to electronics isn't simply "engineering a drop-in replacement". It's a consequence of design trend that resulted in more electronic cars, that have stabilized circuits to run electronics in an electronics-friendly environment in the first place. It's not just flashers that changed, the whole car changed.

If you really want to know how "electronification" of cars went, read about the pioneers. Like Aston Martin Lagonda, it's electrical problems are legendary. When you try to introduce cutting edge before it's ready - this is what you get. That's why old, tried and true tech remains around so long.

Second, they require the right wattage bulbs or they'll flash too fast/slow, and for this reason you also need a second one for hazard lights use.

This argument is moot. The fixture requires correct wattage, it's stated in the manual, which is probably mandated by traffic code compliance. There is absolutely no reason to put any other wattage.

Today, we have other light sources, like LEDs. But their radiation patterns are vastly different, so you can't actually substitute a LED "bulb" for an incandescent bulb. (Sellers say that you can, but you'll never know if you got a proper beam until someone measures it.)

A last argument against thermal flashers is that they waste more energy, although this is probably negligible.

Yes, it is. Compared to the power draw of the bulbs it's blinking, it doesn't matter.

First of all, thermal flashers do NOT blink faster when a bulb blows - they flash slower. Bulb-out indication by "hyper-flashing" is a function of electronic relay flashers and some solid state flashers. Thermal flashers and electronic relay flashers can both suffer from corroded contacts. Electronic flashers can function with no solid state devices - just a simple R/C network or LC network - often using the coil of the relay as the inductance, or the lamps as the resistance. These are DIRT CHEAP to produce and basically bomb-proof as well as being non-polarity-sensitive.(and load sensitive to one degree or another)

Solid state flashers, up until a short time ago, were much more expensive to produce and polarity sensitive and totally incompatible with high current or momentary short circuits. A simple 2 terminal solid state flasher can now be purchased for as little as $2 out of China on Flea-Bay or Amazon - much less than the component cost in quantities of less than 100 - but many of them are still sensitive to overload and polarity. For a little more you can buy "overload protected" and "polarity agnostic" solid state flashers that work with LEDs - not even requiring a separate ground wire - which do not clock or buzz to indicate they are on. These require 2 flashers to provide emergency flashers. More common today are "integrated" electronic flashers that combine 2 flashers in one unit - and now "indicator lamp controllers" that do ALL of the switching in the unit - with low current control switches grounding inputs for left, right, or Hazard functions (generally used only with separate brake lights) - or even the flashers integrated with the "Body Control Unit" computer and even run on the CANBUS system.

Necessity being the mother of invention, these technologies FINALLY made the thermal flasher totally obsolete.