I agreed with whoever posted it that the DMG did in fact say that. So there are in fact other reasons that one spell to go to remove villages.
1) The spell.
2) Ingredients for potions.
3) Components for magic items.
4) As a last supply place before heading into the beyond to search for whatever.
5) Whatever other reason might bring them out that way.
So, I am disingenuous because you remember someone posting something that I never said but you agreed with?
Because that was my question in that quote, not what other things wizards might want to go to villages for. And the point I was referencing stills stands. Only a single PHB spell.
Also
4) Remote villages might not be supply points before the frontier, they may just be remote. Also, if they are remote, tiny villages, then there may not be much point in supplying there because they don't have supplies you need.
5) "and whatever else fits" is a poor argument
2 and 3 are the same thing. Also, reading the DMG section I believe you are referring to leaves that entirely up to the DM's discretion. So it is possible that a wizard might be looking for ingredients for magical items, or they could not. I mean, your standard full caster (since it isn't just wizards) doesn't have a need for a flametongue sword, and they can make plenty of money for an aristocratic life style by just casting 1st level spells.
So, if a DM doesn't require special materials, that falls through on your travelogue casters too.
The numbers would steadily increase over time, yes. People with at least a bit of magic would be fairly common, not relatively rare.
Would they?
You haven't proven it, you've just stated it must be so. Are you familiar with wealth? Wealthy people have existed for thousands of years and we haven't seen massively more people become wealthy, even though wealth is directly carried down family lines through inheritance.
We've already covered that over time, knowledge can be lost. Kingdoms falling to war, and their stores of knowledge are lost. Including the knowledge hoarded by their elite.
Why is magic, which is not directly inherited like money, somehow different than these two examples? Why
must magic spread until it is common? Your only defense so far is that "well, a wizard teaches their child, who will teach their child, who will teach their child" which does not follow.
In fact, we can prove it does not follow because of politics. Thomas Jefferson, massively influential politician. His descendants are not major figures in politics. He helped build this country, if your theory held true, I should be able to easily find his descendants working in the government. I can't.