> I trust a somewhat skilled mechanic more to get his car modifications reasonably safe, than a random software modification
Those are not comparable things. The correct comparison is between a mechanic and a programmer (after all, anyone who modifies his software is a programmer, perhaps an unskilled one), or between an automotive part and a piece of code. Using the correct comparison, we see that we already permit anyone to work on his own vehicle, and that he can put anything in it he wishes. Software should be no different.
> Then, there is the problem, that mechanic parts are easy to inspect
Some of them are. Some look just like the correct parts, but were manufactured to incorrect tolerances. These parts wouldn't be obvious in a visual inspection.
> software modifications are pretty impossible to detect. Short of checksumming the whole car software, it cannot be done.
Software hashes aren't rocket science: your post & mine were both hashed at least one. Indeed, software hashes make detecting changed software easier than detecting swapped physical parts.