Considerable amount of plane crashes, including deadly ones, involve engine failure - often due to things that aren't present at all in automotive (or marine or industrial) use.

Sure, but this doesn’t mean that private pilots need or want FAA to “helpfully” force them to use older tech.

The argument I responded to was about negative externalities of potentially less safe new levels plane engines for third parties. I claim that these are negligible, because the risk of the worse engines is entirely internalized among the plane occupants: with less safe engines, more people will die, but these will almost certainly be plane occupants, not third parties. Third parties do die in plane crashes sometimes, but this is either caused by pilot error, or technical failure causing the plane to be uncontrollable, not failure of the engine. On piston GA planes, control is entirely independent of the engine.

Ability to safely bring down a plane does depend on availability of engine power, however, as lack of it can greatly cut off possible options not to mention engine can fail in such a way that you won't be able to recover before stalling.

FAA doesn't force them to use older tech, anyway. It's just that a lot of smaller planes coast on grandfathering of older engines. Believe me, a lot of CAAs would simply love it if they could force removal of carburator-based engines outside of museum planes, because carburators are one of the core causes for engine-related crashes in GA, and requiring injection based systems would reduce a whole subcategory of accidents.

Thing is, FAA and other CAA are only requiring that you do follow through sometimes ornerous but generally sane testing requirements if you want to bring a new design. This causes considerable up front issues for new designs, but there's a reason why there's much less complaint about it than one would imagine - the ornerous rules are for when you want full certification for the plane, not any of the lower classes. TFA author was trying for full certification, so that the resulting plane would be fully usable without special allowances for flight training for PPL(A), not any of the lower-category licenses. For just flying once you have a license, the requirements are less steep. [1]

[1] My father is currently rebuilding a crashed Cessna 152, question of how deeply tested the engine will be (and thus whether the resulting type certificate would allow PPL(A) training) were discussed a lot

But that’s the entire point: the planes are using those museum piece engines purely because these are certified, and certifying new engines is an extremely hard, close to impossible proposition from business perspective. Sure, there is a way to work around the overly onerous (the mere fact that almost no new piston engines are getting certified is a clear proof that the requirements are excessive), but what would be great is if we simply could innovate in GA like we can in cars or boats or electric scooters.

Car engines, scooters, or marine engines don't have a tendency to kill user if they fail for any reason.

Also, the real reason there's almost no new piston engines is that there's no real demand. Especially since you need to certify the plane with the engine as well. Thus we face mostly incremental changes, because any single development won't bring enough demand to justify the changes. Meanwhile there's not enough money in the market to actually try banning the old engines unless you want to cripple a whole sector.