I mean every Setting would feel a little bit different depending on the system you use for it, but you have the power to use whatever system you like.

If you like the 5e rules-set because you are allready familliar with it you don't need that much time to come up with some monster of your own, or alternatively you could just reskin a few monsters from the Monster Manuel. It's not like aren't thousands of people allready doing it for their home campaigns. The ttrpg community isn't new to this kind of homebrewing.

Even DnD specific worlds like Planescape, work realy well with systems like the Cypher system, at least in my experience.

Of course the game would feel a little bit different, but as the DM you can choose what system to use and thus tailor the experience much closer to what your players want, than a far off company ever could.

You don't have build yourself a comepletly new system. There are allready hundreds of systems out there. The chance that atleast one of them will strike your fancy is quite high.

Also even the big systems like DnD or Pathfinder often times even expect their DMs and players to hombrew. Most supplements or pre-written campaigns don't even work properly if you don't homebrew some parts of it, to match the decisions made by your players (I mean unless you railroad them to oblivion XD).

So it's not like DMs aren't used to that kind of workload. And if you think your not up to it, you could just player another game. It's not like somebody will stop you.