I just don't understand why that can't be the Fighter. Why does the Fighter have to be relegated to Little League while everyone else gets to play pro?
Because that is what people want, and it is not everyone else that is pro. Monks, Barbarians, Artificers and Paladins are little league too. Bards, Warlocks, Rogues and Rangers are AAA and only Wizards, Sorcerers, Clerics and Druids are majors.
Most of the people playing fighter are playing it for the theme and are not bother by being little league or in some cases embrace it. Meanwhile others would be very bothered by fighters moving up.
We want the current fighter. We like the current fighter right where it is.
One of my groups tried the new weapon mastery one session and decided we did not like it for fighters even though it improves "balance". It changed the feel of Fighters and Barbarians into something not as fun for the group. We decided to keep it on Monks and Rogues and we also expanded it to Sword Bards, Valor Bards and Hexblades because it felt right on those builds. That is what feels right to us, and I would imagine a lot of groups are that way.
What do you get from FORCING people to never get to participate in most of the game?
No one on my table is ever, ever forced to play a fighter. No one.
In every table I play (which is many), players play what they want. We don't tell anyone "you need to be the fighter" or "you need to be the Cleric because we don't have a healer" and I would walk away from any table that did. Part of player agency is being able to pick what you play REGARDLESS of party make up or what the other players want. In 1E clerics and Monks were really awful and after we figured that out no one played one .... ever again .... and we had a lot of fun. 5E Fighters are not nearly as deficient as those classes were, but even if they were, all it would mean is that people who did not want to play them would not play them, no one would be forced to play them.
I would estimate that over 70% of the people I have played with in the last 43 years are introverts and they generally do not want to be the center of attention all the time. The idea that everyone in a party actually wants to be a central or equal player in the game is very flawed. That may be true if you have a game full of extroverts, but that is very rare and when it is the case the easy fix is to pick a class so you won't be overshadowed. If you don't believe me look at ANY streaming game online. You will see a variety of players who are clearly not all contributing in equal amounts. Usually this has less to do with the classes than the players, but the point stands players contribute at different levels in game.
This brings the final point - being overshadowed in a bad way is always due to player behavior, not character abilities. The 6 Charisma Barbarian who walks into every role play moment and starts threatening people when literally everyone else at the table is mechanically better at this and others are trying to get in a word. That is what causes bad experiences, not the Wizard fireballing 10 Orcs when the fighter only got to kill one on his turn. When the Wizard throws a crowd pleaser the whole party including the lowly fighters cheer, they cheer when he casts knock, they cheer when he charms his way past a guard instead of letting the Paladin try to talk us past. They ask him to use Arcane Eye to scout the dungeon ahead of time instead of risking the Rogue scouting. The players want this even though it overshadows their own character abilities!