Gotta say I really don't know what you mean here. What kind of processor -- are you talking about effects, or a modeling processor like AxeFX or Kemper? What do you mean that you plug your amp into your guitar through an aux cord -- did you mean to say you plug the amp into your computer? Also, what people? And what really is "studio quality" anyway?
The right answer is always that you don't need anything except whatever it takes to get the sound you want. If you like your sound, then that's great. If you're not getting a sound you like, try something different.
My normal setup is pretty simple. Usually I run my guitar into a noise gate and sometimes overdrive or distortion before the amp (depending on what amp I'm using). I'll aim a dynamic mic into the speaker cone -- close, and a bit off center because straight down the middle gives me too much high end. I'll fiddle around with mic position (and amp EQ and gain settings) until I find a frequency balance that sits nicely with the rest of the mix, then double-check that my amp and interface levels are playing nice, and it's off to the races. So that signal path is guitar > maybe some pedals > amp > microphone > interface > computer. I've often done bass the same way, but I've also gotten great results with splitting the signal and running one channel through a modeler for a big, steady low end, so the mic doesn't have to do all the work.
I've also just slapped a mic in front of whatever I was playing through without giving it much thought, and sometimes, serendipitously, gotten great results. Alternately, I've wound up having to redo all the tracking and wished that I'd spent the time to get it right in the first place. I know people who use two or three mics in different positions on the speaker cabinet; people who run through modelers; people who go totally direct and use amp modeling software after the fact. Some sounds on famous records came from just plugging instruments straight into the mixing board. Do what works for you.