I don’t know where you live, but in hcol areas mechanics won’t even pick up the phone for that much. So you have to get dealer/private seller to agree to take the car to that mechanic for inspection.
In a hot market if the car is priced reasonably there’s 5 other people in line to get it without inspection.
And then even if you can get the car inspected, mechanic offers you no guarantees. What do you think will happen if your engine explodes a week after you buy that car? You think that mechanic will replace it for free because he missed a big issue?
Your suggestion is awesome if you have a mechanic in the family or as a close friend you can trust. Otherwise just money down the drain really.