I think we agree that specialization is a great idea. Where we seem to differ is the point in a player's development when this specialization should occur.
Having a player specialize in playing a particular position at age 14 is really not stupid at all. Coaches do this all over the world at this age. In general kids are starting to play the game a bit earlier and by the time they are 14 they really need to start focussing their attention on the demands of a specific position or positions.
The BPL examples you cite are interesting observations. I think that coaches end up moving people around as a neccessity and not necessarily by intention. Usually it is due to injuries and sometimes lack of depth in certain positions. The movements are usually natural transitions as well. A defesive mid can easily transition into a centre back role. An outside back could play winger in the modern game. What makes the player able to play the alternate position is rarely because they have "tried out" all the positions on the field. Rather it is because the positions have common core requirements that a player already possesses.
Total Football is a great system that was most successful in the 70s. Its successor Tiki-Taka as demonstrated by Barcelona stresses ball movement as opposed to positional dynamism. I am not aware of a team in the world premier leagues that currently uses a pure Total Football approach. Yes the elements of midfielders covering for outside backs etc are part of the game but these are now expected elements of the midfield positions and should be taught as part of that position.
To be clear, I am not saying that versatility is not important. Specialization doesn't preclude versatility. The really special players of the game are versatile specialists. Let's not confuse specialization with lack of creativity. Those are two orthogonal thoughts. Being a specialist enables the player to play with flair, expression and imagination. It gives one the freedom to be creative.
Good coaches know how to identify players whose skill sets make them good candidates for playing multiple positions and will provide the opportunity to those players. This helps to increase the versatility of the players and to provide the team with more depth. This is also different from having all players try their luck at playing every position on the field.
The USMNT could use more specialists at all positions in my opinion. What if we had a true number 10 with fully developed play making skills? What if our forwards were real specialists at taking on and beating 1 or 2 defenders?
what if we had a real specialist of long range shots who could drive balls into the net from outside the 18? The USMNT team has a few problems but I don't think an over-abundance of specialists is one of them.
To play at the highest level in the modern game, by age 14 or so, a player needs to know where they belong on the field and should be working really hard to master both the technical and tactical skill needed to make them successful in that position.