Whereas I think people enjoy those games at your table because of the people and environment, and because playing group role playing games is fun, not because those systems are good. I’ll enjoy a game of 3.5 or Pathfinder with a good DM and group, but that doesn’t make them good games, or that I need to play them occasionally in order to get 5e.
But more to the point, two things:
1) It doesn’t matter why sorcerer exists. They’re a strongly archetypal character concept that has mechanical distinction in the game, and it is important for that to continue. It’s better to leave the concept out than to try to force it into the same class as the wizard. Same for Bard, Warlock, Cleric, and Druid. How it came to be a distinct notion that people expect to be mechanically distinct is only relevant in an acedemic sense.
2) Those classes, and the mechanics invented for them, exist because the concepts behind them already existed and people wanted to play them as distinct entities from the wizard. They could have simply called the “at will spell guy” some bland synonym like “arcanist” or something, but people wanted to play a user of forbidden magics, who’s power came from dark deals with dangerous powers rather than from study, and who broke the normal rules of magic. The sorcerer exists because people wanted to play a guy who was born with the ability to use magic, and who does so without training or study, and their idea for a different way to learn and gain spells fit the concept.
These aren’t concepts that popped into being during the mechanical design process. They existed before the mechanics, and have taken more specific and traditional shape over time because people are used to the pairing of concept and mechanics, but the concept exist before and outside of DnD’s history. The mechanical concepts would either have been alternate wizards or just not published without the thematic concepts.
For a DnD Light, meant to look back to the bare class simplicity, though, I think the “basic 3” is a great way to go. It certainly works for Dragon Age (although specialization in that game series replaces subclasses).