games

They don't. One of the many, many things that sucks about D&D is that it's the most recognised, so people think it's a good place to start with TTRPGs.
It's not. It has most of the complexity of a crunchy game like PF2e, but no mechanical unification, so every action has its own rule, rather than similar actions just being small variants on the same. Rules are often specific, applying only to certain situations, but still vague, forcing the DM to decide how they're actually meant to be applied. Similarly, it's very crunchy and combat focused but combat is pretty barebones, just being a case of standing in front of an enemy and hitting it until one of you falls over. Could be either you or the enemy, the balance is skewed at best.
As if there weren't enough mechanical problems, the lore stagnated after 3.x, and wasn't that deep even then; The Forgotten Realms setting in particular is extremely barebones once you're off the Sword Coast, and regularly leans all the way over to downright offensive. Like ye olde minstral show racism in stuff printed in the last 5 years. And they charge you a fucking arm and a leg for everything, so, like you say, you need to pay like $150 just to play in a homebrew setting.

You don't want to play D&D. If you do, you want to play Pathfinder 2e, Savage Worlds, or Shadow of the Demon Lord/Weird Wizard instead. Pathfinder in particular has great fey lore, even if you pick a different system it'd be worth looking at Kingmaker for fey storyline ideas.

What you probably want is something like Fate or Monster of the Week, a more storytelling focused system that isn't so balanced around parties. FitD games would also be worth looking at.