Needless to say, I have a somewhat different view about RPGing. I don't find the comparison to physical prowess in sports all that helpful; and I would associate differences in temperament with differences in characterisation and participation in the game, but not with whether you can play a magic-user or get stuck playing a fighter.Maybe, but I don't think one player needs to be able to effectively play anything close to the full range. It simply needs to enable the characters that the particular player is interested in and suited for.
For example, (American) football posits a number of roles. If I'm a 6'8", 350 lb. giant, not all of those roles are for me.
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Similarly, in D&D, if I'm someone who likes to spend hours poring over books and preparing an optimal strategy, I'm probably a wizard, maybe a cleric, conceivably a rogue, and probably not a barbarian.
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In none of those cases do I have any expectation that any iteration of D&D would be able to match all players with all possible characters, nor do I understand the origin or the value of said expectation.
I don't see that arcane has to be quasi-science. And in B/X the only power that you describe here that is routinely available to PCs is Raise Dead, and that's divine!D&D posits the arcane (quasi-science)/divine magic distinction, magic that can take you to different planes of existence, raise the dead, or grant wishes, and a player's handbook where all of the above are presented as achievable character abilities.