]Average level of spellcasters in a village of 200:
Adept: 1 1st-level
Bard: 1 1st-level
Cleric: 1 1st-level
Druid: 1 1st-level
There may or may not be *any* Paladins, Rangers, Wizards, or Sorcerers (the average roll is negative or zero, and the table doesn't say what to do in that case).
...which sort of shoots down the idea that, in the default D&D universe, magic is so rare that many communities don't have spellcasters. As we see, even assuming that you didn't roll ANY paladins, rangers, wizards, or sorcerers, a small village is going to have (on average) MULTIPLE spellcasters. No, they're not world-shakers, but the notion that magic is so rare that the typical inhabitant isn't even aware that it exists simply is not supported by the rules.
On the other hand, in a city of 10,000:
Adept: 2 9th-level, 4 4th-level, 8 2nd-level, 16 1st-level
Bard: as above
Cleric: as above
Druid: as above
Paladin: 2 8th-level, 4 4th-level, no others capable of casting spells
Ranger: as above
Sorcerer: 2 8th-level, 4 4th-level, 8 2nd-level, 16 1st-level
Wizard: as above
So, no casters above 9th-level (meaning 5th-level spells are incredibly rare, and 6th+ are unheard of), and less than 2% of the population is made up of anyone that can cast spells at all.
...of course, that small city COULD have a cleric of as high as 12th level. Bump up the population a mere 2,000, and all of a sudden, that city could have a cleric of 15th level.
And we're not even TALKING about the big metropolises here--we're talking about cities on the border between "small city" and "large city."
Plenty of spellcasters to make the population well aware that magic exists--and the sorts of spells we've been talking about (flight and fireball) are likely to turn up, on average, even in a large town.
As I said: you may think that magic should be extremely rare in D&D, to the point of being unknown to most of the population, and that's fine--but that's not the default assumption they used when designing the game, and it's certainly not the default assumption for the published settings.