A couple of times, I've been fine with buying the car first, but with a clause in a sales contract saying that I have the right to return the car within 3 days for a full refund (basically replicating the effects of my state's lemon law. The lemon law only applies to new car purchases).
But the mechanic's check has never actually revealed any issues that the seller hadn't already disclosed to me. People tend to be pretty honest about those sorts of things.
"I'm looking to buy a used car and wanted somewhere to give it a once-over? Do you do that? If so, how much and do you have availability on (day)?"
I've never been burned or disappointed buying from a real person. I've bought two cars from used car dealers and deeply regretted both of those purchases.
And yes, you might have to pay taxes, but you get that with the dealership as well. Dealerships aren't immune to taxes.
More reasonable people acknowledge that there are obligations both ways: Society has an obligation to the individual (private rights and ownership), and individuals have an obligation to society (taxes and limitations on what you can do to private property).
I do agree that sales taxes seem kind of weird and arbitrary way to collect society's obligations. Personally I prefer something along the lines of Georgeism, where only property is taxed. This makes the ownership / taxation thing symmetric.
If you aren't getting much value for your taxes, perhaps elect better people to handle that tax money.