This post by Alex319, in the "How much do characters know about game mechanics?" thread, may be illuminating.
Darjr, I think you overstate the matter in the first place with the assertion that the rules somehow make the attainment magical by default.
Is it possible to become a world champion weight lifter while holding down a job as a computer programmer? Perhaps in theory, but I doubt that it has been accomplished. Common sense and life experience suggest at least that it is highly unlikely; such a physique requires dedicated effort to develop and maintain. So does the expertise of a top-notch programmer ... or that of a D&D cleric, magic user or thief.
That -- not magic! -- is the underlying rationale.
In strict realism, perhaps even the fighter should be too preoccupied with other matters and only NPCs whose sole occupation is weight lifting should possess such scores. However, this is a game inspired by a fictional genre in which warriors of legendary strength figure prominently.
Perhaps the most renowned of all had a career that might best be translated into game terms as "dual class" from thief to fighter. Such a worthy is even more extraordinary than a single-classed fighter with 18/xx strength, as reflected in the requirements for the attainment.
Does that suggest that an extraordinary non-fighter should also be able to develop such strength? Should one decide that it does, then one might also bear in mind that by the rules as written there is a cost associated in the dual-class (for humans) or multi-class (for fey folk) structure.
Offhand, I can think of no example from classic sword-and-sorcery fiction of a musclebound mage, and doubt very much that such a figure would not also be a puissant warrior -- but it is your prerogative as Dungeon Master to make such allowances!
One might also note the statement in the PHB that "strength is a measure of muscle, endurance and stamina combined." The implication is that a character might be more gifted in one of those aspects, and less in another, than the composite score suggests. Although employed so rarely as generally to be forgotten, that option is present for any DM who finds it worthwhile.