Hiya!
No OPTIONAL Feats and no OPTIONAL Multi-Classing. Problem solved. Literally. POOF! Fixed.
I understand your rant...glad you got if off your chest. Nobody likes to be trying to run a game with "ZYX feel" and players wanting to play in a game with "CBA feel". Just not gonna work 9/10 times.
BUT...and here's ticketey-boo of it, MC'ing is optional. I mentioned Feats as optional as well because I don't think I've
ever heard of a DM who allows one but not the other; the
entire point of Feats/MC is to "build a specific, unique and interesting Character". But that's just an illusion. Why do we have the term "Hexblade" or "Sorlock"? Not because they are "unique and interesting Characters utilizing optional rules in the game"....nope...it's because of the
EXACT opposite; Feats/MC actively encourage a very specific, very non-unique, series of "character choices". "I take Class X to start, then Class Y to level A, then Feat #1, then Class B, then Feat #2, then....."; that's not "unique", that's preplanned and the same as everyone else.
It's a hard pill to swallow for a lot of DM's, but... IN MY HUMBLE OPINION! ...Feats and MC in 5e are done completely wrong and do the opposite of what they were trying to supposedly do; and this translates into nothing but annoyance, bad feelings, and tears from both sides of the screen.
My Suggestion? "Ok guys...we're gonna try a Core Three, no Feats, no MC game this time". Then make sure you let Players have their PC's
try to do things that would have normally 'required' a Feat or MC combo, or something from one of the 'other' books. Give it a DC, let them roll. When they pull these things off, they will be thrilled and actually feel like freaking Heroes. Not just "Oh, yeah, well, duh... I'm a level X/Y Z Class/Class/Class with Feat A and Feat B, and Abilities #3 and #8"...because at that point it's, literally, "Yeah, you and EVERY OTHER character with those exact classes, levels and feats...which is every other character with those classes and levels".
Ok. that was MY rant.

I don't like Feats or MC in 5e (or Feats in ANY version of 'D&D'; I am a fan of MC'ing in 1e/Hackmaster though...).
^_^
Paul L. Ming