All excelent points.
Regarding Pic/Weaver rails, a good scope, with good rings can often be removed and reinstalled with a high degree of repeatability.
Even with light recoil on a .22 I have seen claw mount dovetail rings walk. I have not seen this recently, because I learned early on to put a drop of locktite on the claw for a bit of stick.
Good rings are indeed important, I use "Weaver" brand, they are comparably priced with cheap rings, but are well made and work. With cheap rings that I have tried, tolerances can be a bit "wide + and -" on both the bore for the scope tube and the clamps. I had tried a cheap gunshow one piece mount, and was unable to zero the scope, it was that crooked from the factory.
Bottom line, you want a good, solid and robust connection between you optic and the rifle as that is one less "variable" to contend with when it comes to accuracy.