Picking magic items so fighters can fly, etc. as others suggest means those items are part of the game, which the DM (for whatever reason) might not want. Also, the DM can remove any spell from the game for any reason, so even if you play RAW and allow casters to choose spells when they level, the DM really has final say.
Like in life, the players purview is deciding what their characters DO, not what they GET. Some DMs don't play that way, I do.
Well, for one thing, our house rules curb the power of casters, especially in tiers 3 and 4, and have (in one fashion or another) for over a year now.
Well, you can do a melee / ranged DEX build or a melee / thrown STR build or split the difference.
For example, instead of trying to have a 16 in STR or DEX, I'll have a 14 in both. Sure, my bonus is -1 compared to the optimized build, but they are weaker in the other way by typically being 2 or 3 less, as where I am +1 or +2 better than them.
It is just about balance instead of optimizing IMO. One of my favorite point-buy arrays is 14, 14, 14, 10, 10, 10. Now, even without racial ASIs I can be +2 in three things which are important, but no dump stat penalties. And with the +2 racial ASI, I can still have a 16.
If I do the racial ASIs right, I can even have 14, 14, 14, 14, 10, 10.
Not if you already have weapons out, like when you are carrying those extra 2-3 spears in your shield/off-hand.
Also, Dual Wielder allows you to draw two weapons. And IIRC WotC has released either feats or fighting styles in later publications which allow you to draw a thrown weapon as part of the attack.
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.
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.
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.
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.
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.
The fighter is supposedly the best at combat, and that supposedly justifies their virtually non-existent utility. But they're really not.
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.
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.