To add a bit more...
Car engines are used to some degree in amature build aircraft. Subaru engines in particular.
For the "certified" world, the certification requirements for the airplane require that the enigne( s) also be type certified. This is very costly. Yes, it is possible, but it requires the co-operation of the engine manufacturer, and my experience has been that auto engine manufacturers have extremely little interest in what they perceive to be the liability associated with the aviation industry. Large cost, large risk, very small market.
Deisel engines create very unwelcomed impulse loads into propellers, and the troublsome gearbox of the Theilert was only a partial solution of apparently limited life. There is a future here though....
A few lingering airplane certification requirements ramp up the challenge to this, one of them being that the engine must be able to run with no extrenal electriciy applied. some FADEC aircraft seem to have gotten around this somehow, but the certification requirment remains applicable.
Aircraft engine design and car engine design took very different philosophical directions some long time ago. There seems to be little financial incentive (deep GA aircraft market pockets) to bring them back together. If we cannot simply get a 100LL Avgas replacement sorted out, how will we ever cause a wholesale shift in engine design philosophy?
That said, I have an order in for the first available SMA deisel engine for a C182 project for a client. But, the SMA deisel is not a car engine.
(5000 rpm would destroy a standard propeller).
Presently available propellers cannot be operated at speeds greater than their design speed. In general, you cannot operate propellers with the tips going supersonic. If the prop will do it a bit (ever heard a C185 floatplane?) it certainly won't go anywhere near that much faster. Whole new propeller, or propfan designs could work, as long as they can pass the rather rigourous noise testing requirements. However, their small diameters proabably would not work well with existing piston engine size, or cowling arrangement. Propfans have had some success with slim turbine engines, but that's a whole different issue....