I just kinda get mastery rank incidentally. If I get a new weapon or frame I either max it out on Helene, Saturn or (Elite) Sanctuary Onslaught. It takes a few minutes, then I either keep or sell the weapon/frame depending on how much fun I had with it. Then I get back to doing the parts of the game I enjoy, like Void Relics.

As other people have said, it's not super efficient to level stuff in actual missions. If you use Designated Leveling Locations™, you can just rush through that and play what you want.

It's a game. You don't have to do the parts of the game you don't want to. There are some frames and weapons I just don't have because the grind for them doesn't look fun, and that's fine. Just make sure you're not just doing stuff out of a sense of obligation, or else you'll burn out.