In an effort to offset the extra equipment in my RV-10, I decided not to prime most of the alclad. Not trying to fuel the primer wars, because my RV-6A was fully primed. However, there are some exceptions. The battery box, which I modified for a larger 24V battery, is powder coated. This was prompted by the condition of the battery holder in my 1965 Chevy pickup; it looks like the battery was a magnet for grime and corrosion. I went ahead and powder coated the mount for the O2 tank and other mounting pieces of thicker alclad material. And I also powder coated the brake reservoir bright yellow, the better to see brake fluid. I'm lucky to have a good coater nearby who serves the local automotive and aviation industries. He also did my engine mount after I had the reinforcement SB done and my steps, too.
On the other hand, I had the control stick mounts machined per the plan recommendations and decided not to paint or prime. Nor did I prime the F-1065 pushrod as those parts are easily to inspect and are well protected inside the fuselage. The tube pushrods are primed and the other extruded pushrods will be powder coated. I also do not prime fluid tubes; it's too easy to disrupt the paint/coating/whatever during installation anyway, especially if you need to flare an end after the tube is in place.
My point is that, even if you prime 'everything', there is no single mindless approach, as people who have inadvertently primed the inside of their fuel tanks have come to realize. You should consider the part's application and environment.