Well obviously, you can run anything.

But I don't think your diagnosis of people's difficulty with low magic is correct.

Magic is so inherent in DnD's classes and monsters that most of them are going to feel very out of place in low magic settings. It's hard (for me at least) to justify how dragons or giants or beholders haven't conquered all of civilization if magic isn't somewhat common.

Also you are very limited in your class choices if magic is supposed to be rare. Wizards are especially vulnerable, as they depend on magic being common enough for them to find scrolls and spellbooks to copy from.

I guess the big problem is that, even if your campaign is low magic, your session will probably still be very high magic.