What about all those slides, pushes, pulls, and various micro action types like reactions and interrupts?
They're just handled by more specific rules/rulings. Thunderwave, for instance, still pushes, in spite of there being no formal 'push' jargon or involuntary movement mechanics in 5e. Reactions already exist 'interrupts' are just a special case-by-case exception to the usual use of your reaction, and bonus actions have been added, as well.
Still, it really needs to remain optional so that it doesn't conflict with TotM game play
Anything and everything added to the game after the PH is necessarily optional, so that's a non-issue. And every to-the-foot range/move, encounter with more than one enemy, detailed battlefield, and geometric AE conflicts with TotM, anyway, so a non-issue with a non-issue.
It's not a problem for a red dragon to hit you
Didn't say it was. But you are getting hit more often, not less. That's not exactly advancement (at least, not for you). Sense of advancement with accuracy bounded, of course, comes more from hps/damage.
just like it's not a problem to fail a saving throw.
Oh, that can be an issue. When hp scaling comes into it (save:1/2, for instance), it's fine, humiliating to be getting steadily worse, but at least you're also getting steadily tougher. When the save is binary and doesn't involve hp scaling, it's a lot less fine.
and you're not "behind the curve" if you have a low AC or lousy saves. You're just playing the game in a different way.
Well, you are playing the game a different way, a way that includes being behind the curve - perhaps even reveling in it.