It just takes practice. I've played as many as 16, although my sweet spot is probably 8. When I first started, I couldn't fathom playing 2 at once. But you just work at it, and it comes easier and easier. I'm to the point now if I play only one table (unless it's a league game with a lot of chat interactivity going on) I want to blow my brains out.
As was said, some people just process information faster than others. Everybody has a different limit to what their comfortable with, but likewise almost everybody can learn to play more than they currently do if they just put in the effort to practice. Comfort comes with experience.
As to the robotic play, yes you do (especially at first) need to seriously tighten up and play ABC, but over time you learn that you can actually keep players straight between tables and make some situation-dependent decisions. It's not 100% robotic. Especially with a HUD, which is almost mandatory for effectively playing more than about 4 tables -- at least for us mere mortals. The Shaun Deebs and Nanonokos might play 20+ tables without a HUD, but the rest of us really have no hope of that.
If you're not a winning player already, don't add tables until you are. You're just going to accelerate your losses. When you're regularly winning at a given stake, you can consider either moving up or adding tables. Which one is best depends on you and your BR. Adding tables will lower your bb/100 winrate because you play tighter, but will increase your hourly rate if you remain a winning player. Volume is where the profit from multi-tabling comes from, especially if you're on a good RB or VIP program. A good RB plan can make a break-even or even slightly losing player an overall winner if they can play a lot of tables/volume. The key is to drop tables and/or stakes if you start losing consistently.