For emissions there is often nothing visually wrong with the car. So you’d essentially be giving up on enforcement if you didn’t require everyone to get their car checked at least every few years. Doing it every year is IMO overkill.
As to safety inspections it’s not a very large effect, but they do save lives and the expense is generally rather small. Yes it impacts the poor more, but that’s because getting unsafe vehicles fixed or off the road is kind of the point.
I have never met anyone who properly fixed an emissions problem, and I think that's what GP meant by willful violations. Any car old enough to have emissions problems isn't worth enough to fix properly, so you cheat it by doing things like buying a spacer for the O2 sensor. Personally I'd be shocked if emissions inspections had a significant effect on total vehicle emissions, and I think that the most effective things are done at the manufacturer