A lot of airplanes, both certified and non-certified do actually use engines derived from car engines.
The diesel/kerosene engines from Thielert and Austro Engines (used by Diamond mostly) are based on a Mercedes A class engine. The Austro Engine is still very close to the original engine, Thielert has replaced a lot of parts with custom lightweight parts.
For the certified world with its high development costs, there are a few issues with car engines:
- they tend to be heavy (weight is not such a big issue in a car)
- they are liquid cooled these days (which adds weight)
- they get their power at high RPMs, a typical propeller should not turn faster than around 2700 RPM to prevent the blade tips from going supersonic. So you need a reduction gear which adds weight and complexity. The gearbox is the weakest link of all current car derived engines. Until recently, Thielert required the gearbox to be replaced every 300h (it's 600h now).
- airplane engines tend to operate at around 65% HP on average (constant power setting for hours) while car engines average much lower. Thermal management and stress on the material is a bigger issue therefore, requiring a sturdier construction.
- they have a short life span, aviation is used to servicing engines for 50+ years so as an engine maker you should be able to guarantee parts availability forever
- their advantages are smaller than it looks like, the biggest argument still is fuel availability which is a complete non-issue in the USA where most of the GA fleet lives
The biggest issue is of course the very small and conservative market. There is just no economical reason to move away from the 1940s avgas engines -- for as long as there is avgas available. I guess the SMA engine is promising but it's been an economical disaster so far.
Keep in mind that the avgas engine industry hasn't even managed to offer something as trivial as electronically controlled ignition (FADEC). It could be easily added to their existing engines.