Let me ask a question - how many PC-type spellcasters do you have in a given village? A town? A city?
I think the basic answer for my world to what I infer is the main thrust of your query is that I don't like having a hard, bright line between PCs and everybody else. PCs are certainly exceptional in their ability to progress in their professions rapidly, but in the end, they are special mainly in that they are the characters my players have chosen to inhabit.
Having *player characters* be able to use at-will magic does not mean that this magic is common in the world at large.
I understand that that disconnect solves the problem and that it is fine for some / a lot of people; for me it is not. The "magical abilities curve" that trends down from gods (and perhaps a few villains) through PCs, various strength NPCs and finally to the common folk may be a fairly steep curve, but it doesn't (for me) have any cliffs in it.
If magic is relatively hard and limited for PCs, then I find it easy to postulate that the vast majority of the population have no access to it at all. On the other hand, if even novice PCs can pop off limited but still substantial spells (
Firebolt is good enough to one-shot a lot of common creatures) repeatedly for a more or less indefinite duration, then that says to me that some magics are really quite easy, and so, barring special circumstances, they very likely have become fairly widely known - uncommon perhaps, but not rare. One can, of course, invent fictional special circumstances to rationalize the disconnect*, but I am disappointed to find I am forced to, especially when the 5e DMG seems to promise otherwise, and my sense (admittedly pretty much limited to 1e) of D&D tradition is that it shouldn't be necessary.
Maybe there's a difficulty in getting the setting characteristics across when the PCs are really special people within it? As a matter of course, PCs are dealing with very special situations that most people in the fictional world do not experience. It is kind of like John McClane in "Die Hard" has very violent experiences, when most folks in the US will never experience a gunshot or explosion.
Their choices and deeds will certainly distinguish them (or so we hope). Their abilities may be strong, but should not have to be highly unusual in character.
* Or, of course, resort to the always handy "because reasons".