There's only one RPG system I've ever heard about with that degree of complexity: FATAL. And if you try to run a game of it, you will lose your friends, your SO will leave you, and you'll probably be forced to go live under a bridge somewhere with only the voices in your head (who all sound like Gilbert Gottfried) to keep you company.
Now, now, I'm sure the four people who play FATAL enjoy something about the game as they use their own tears of loneliness to lubricate group fap sessions while they recite how many imaginary women their characters have raped.
Huh. I wonder if anyone has ever thought about creating a FATAL MMORPG as a honeypot trap for all the online misogynist jerks? If it existed, we'd probably never hear from them again until the news reports about dehydrated corpses being hauled en masse from parent's basements across the country...
It's a core element of the game. Not allowing a core element is certainly within the rights of a DM, but he's now created a house rule and that's not something used to evaluate a game, IMO. If you have to house rule something, the core element doesn't work or isn't very good.
Agreed, but it is a problem stretching back to 1e - the basic classes like Fighter or Thief can't keep up past a certain point (level 12+) without being able to throw at least some spells. Oh, what's this, there's a magic using class called bard with both fighter and thief in it that I can choose to level up in..? 2e didn't help it very well, and 3e made it more complicated with the alleged fix of prestige classes.
Another good thing for me about 5e is that multiclassing isn't necessary to get the most out a character. If you want a fighter/mage, pick Eldritch Knight as your Martial Archetype - yes, you're a 1/3 caster instead of a 1/2, but you get other benefits directly related to what a fighter/mage would want.
Sticking with a class to level 20 generally gets a strong benefit - though one thing that appeals to me as a munchkin and fills me with regret as a DM is the Warlock class. Because it recharges its spell slots on a short rest, a lot of long rest dependent classes will take a dip into Warlock so they can cast more spells more often - or in the case of Paladins, use them to fuel Smites. That neglects the flavor of a Warlock, making a pact with a being much stronger than yourself just for a chance
to use magic without long study or birthright...
The short/long rest gap, in which some classes are long rest dependent and others are short rest, is the one place where 5e's balance falls down a bit - and it's a big problem for a Gritty Realism game.