For a market to exist, you need more than demand. You also need supply. The smaller the supply, the less of a market there is. In a low-magic world, trade in magic items is apt to resemble the trade in paintings by the Old Masters. If you want a painting by Raphael, you have to find someone who's got a Raphael and is willing to part with it. Oh, and you don't have the Internet, or even a telephone. Good luck. If you've got enough money and persistence, you can probably manage it, but it will take quite a long time--long enough that abstracting it into a simple "put down your money and take your items" is no longer reasonable.
Absolutely. In a low-magic world.
I would hope that the default DMG campaign world is not low magic, but some middle ground.
In a medium magic campaign world, magic items can be acquired via a few shops in extremely big cities and even some larger towns, and some back alley deals elsewhere.
In a high magic campaign world, magic shops might exist in nearly every large town and city.
Supply and demand as you state.
In medium and high magic worlds, the supply is greater. And even in a low magic world, there would be specialists who can acquire magic items, just like there have always been specialists who could acquire paintings by the Old Masters, even before the Internet and telephone.