There's a pretty significant difference between something that is explicitly allowed (spells) and has to be explicitly banned by the DM if they don't like it, and something that must be explicitly allowed by the DM in the first place.
If I'm playing with a new DM, I don't ask them whether I can take Magic Missile. If they don't allow it, it is upon them to inform the players as such. However, I do ask whether feats are permitted, because they are optional and I have played in games where they weren't allowed.
Well, we're talking about player agency vs. DM agency. For me, it is no contest, DMs win. That holds true whether I am a player or the DM.
My point was just why would I allow something that the player can decide would dictate what happens in the game when it is the DM sets the stage. The players can do whatever they want within the framework their characters experience, but that framework is completely decided by the DM.
Okay, you've got a 14/14/14 split build at level 1. What fighting style do you take? How do you spend your ASIs leveling up? The difference might only be +1/+1 at level 1, but if you keep trying to split your build then you will rapidly fall further and further behind more focused builds.
Look, I'm not going to plan out a full build just to demonstrate how you can have a fighter who is evenly good at both melee and ranged, it isn't hard. Of course, if you hyper-focus on melee or ranged, the other will suffer, but that is the price you pay for being a specialist instead of a generalist.
As for holding three spears in your shield hand, that's very much DM ruling / house rule territory. I realize that you're essentially going for a hoplite concept, but D&D spears are arguably heavier than what they used and a DM could easily say nix the idea.
Yes, that's the idea, but who said spears? Javelins are thrown weapons and held more easily, have a better range, and to equal damage. Regardless, 2 spears is only 6 lb. and you have the third in your other hand.
Also, WotC's design was horrible from the get-go when you talk about thrown weapons. Sure, you can pull an arrow, notch it, draw, aim, and shoot as an action, but pulling a handaxe or even a dagger from your belt isn't part of the attack?
At least Tasha's gives an option for it, but IMO it should just be part of the action, especially if the weapon has the light property. (FYI,
that is one of my house-rules.

)
If the DM said no, even after I showed them how real-life soldiers did such things in the past, I would find another DM.
Also, since I don't feel like making a separate post to address it, the throwing fighting style is a fighting style, of which non-champions only get one. Therefore, you need to weigh the opportunity cost of taking that against the other options you could have taken. Unlike a wizard, you can't simply swap it out the next day if you don't think you'll need it.
If your PC is primarily focused on throwing weapons to deal with flying foes (not a common encounter IME, but it does happen of course), then you take the style to match it. Just like dueling, great weapon fighting (though it sucks), archery, and so on. Any style you take is a trade-off for something you aren't taking--it is the same with every aspect of the game. The choices you make matter.
Wizards don't need to choose between stats to cast spells. They just need Intelligence. It'd be different if you need Constitution for Evocation, Intelligence for Transmutation, and Charisma for Illusions, but that's simply not the case.
I agree to a point, and again that is a failing of the game design. Also, Fighters don't need more than one score either. They have d10s for hp, which is sufficient, can wear any armor as well. CON is helpful, as is DEX, but STR is primary (unless you are doing a DEX build...).
Wizards benefit more from CON for concentration checks and much needed hit points since they only have d6. DEX is also highly advisable given the low hp and no armor, so ACs tend to be low unless you are in a very high magic game...
The fighter is supposedly the best at combat, and that supposedly justifies their virtually non-existent utility. But they're really not.
Oh, I definitely agree! Fighters
should be the best, but for WotC decided to make every class good in combat, so Fighters only (barely) stand out if you want to optimize your build. Again, WotC's design choice--not mine. So, I homebrew and house-rule the crap out of 5E to restore a more balanced game.
Why can the 20 Strength fighter only toss a javelin as far as an 8 Strength wizard? If the fighter is the king of weapons, shouldn't they be better than that? It's not as though it adds any real complexity if (for example) the fighter's throwing range increases by 5 feet for every point of Strength they have. And really, quick draw should be something every fighter gets IMO. They're the weapons guy, let them switch between weapons easily and use extra attack with thrown weapons.
Agree 100%. But, again, 5E is about simplicity. Would it have hurt the game for them to make the ranges a base, but add 5 feet per point of Strength modifier? Of course not! My
Long Thrower feat allows you to double your ranges with thrown weapons, for example. Yes, anyone can take it, but I doubt the Wizard would while the Fighter might.
I mean, think about this, with Crossbow Expert you can use all 4 attacks with a heavy crossbow in 6 seconds! THAT IS ABSOLUTELY BULLSH!T! It would take a 2-3 rounds (most often longer) to load and fire a heavy crossbow if the game was designed to model real life.
So, yeah, 5E has a lot of crap rules... no shocker there.
Both Strength and Dexterity fighters should be able to be effective in melee and at range. Then, if you want to specialize in one over the other, you should be able to be exceptional at it. Not losing 50%+ of your damage after 4th level because you didn't want to take the thrown weapon fighting style.
Not really. If you have a better STR, you should be better at melee, and a better DEX at ranged.
Otherwise, I agree, thrown weapon rules (along with dozens of others) in 5E are garbage really, but that is what over simplification gets you. So, I answered the questions with options as they are in the game, the fact those answers don't satisfy you (or others) just shows how poorly the rules work as they are.