If you want something simple, you could try Peril in Pinebrook. It was designed to be used in schools to teach kids to play. It uses a much simplified set of rules and pre-generated characters. I’m going to be using it with my family in a few weeks
5e is fantastic. It presents the standard combat-centric D&D rules, and provides a lot of freedom for players and DMs to fill in whatever rules they find most enjoyable.
Levels 1-3 are designed for the express purpose of onboarding new players, so complaining that it doesn’t fully represent D&D, is pretty silly - it’s supposed to be simplified.
I will agree with the facts behind your comments on the skill system, if not the exaggerations. I would prefer a looser system, akin to those from Fate, Cypher or Daggerheart, to allow for more creative freedom.
D&D doesn’t suck - it’s a combat centric system, as it always has been.
I can’t speak to how well 5e would work with dark sun, but 5e is very much about epic heroism. Levels 1-3 exist entirely as an introductory system to avoid overwhelming new players - IIRC, there are official suggestions to just skip them if playing with experienced players. Additionally, they are designed to go incredibly fast. The meat of the game really starts after that, and the characters quickly catapult to functional super heroes.
If you wanted to allow customization but without user accounts, you could just store all that data in a cookie on the user’s machine. Just make sure you put clear warnings about how the data is stored and what will be gone if they delete the cookie