It depends how you build your classes. If you got 20 classes but they only take 1-2 pages each, is that more or less simple and streamlined than the current PHB?
I can't answer that with knowing how much design space your 20 classes cover. What your system should be going for is covering basically any type of character concept that player brings to the table that fits with your fantasy theme. And if your 20 1-2 page classes do that, then great. But my suspicion is that either the classes will be so narrow that you are just fitting into one of 20 inflexible archetypes, or else that your system is so generic that everyone is using the same mechanics with different color, or both.
I don't believe that there is a "I just want to attack" class. I don't think that's a class concept. I don't think that's a character concept. "I want to be a master of weapons" is better, but hardly sufficient. For that to be sufficient the whole game just has to be about combat with no exploration, no social interaction and intrigue, etc. Or else the things that aren't combat have to be so trivial that you can get away with having one member of the party useless in everything that isn't combat.
You need to have a class that can cover everything from being a pirate to a courtly knight. And that's not that hard. That's just selection of skills and feats with the core idea of, I'm a competent warrior in every respect. Because both those characters as they level up can transition into being lords. The pirate is captain of his own ship. The courtly knight gets a castle and retrainers and an army. You don't want a class that is forced into being a lackey - some more important figures meat shield. If the player wants to go that way, then fine but that's not what the Fighter class should be designed for.
As for your spell lists, I think you are using legitimately bad design to justify more bad design.
Like what if my player comes to me and says, "I want to play Elsa". In my system, I say, "Great. You want to be a natural Cryomancer. Get a sorcerer. Take the Frigid bloodline. Take the Elemental Mastery feat and choose 'Cold' as your element. Take Spellcasting Prodigy as your trait, and then pick up any spells that you think complement your cold theme. When you do magic, we'll flavor it as if everything you are doing is ice based. So like when you cast Mage Armor, we'll flavor that as you are covering your body with ice in response to attacks."
But if have the same player come in and I have 5e, well "Wall of Ice" and "Freezing Sphere" is exclusive to the Wizard list for who only knows what reason.