Keep in mind that I'm talking only about the PC version since it seems we're talking about that version, and that's the only version I'm actually familiar with.
What should just be done is make setting up a gamepad more obvious: Rather than have them look through multiple options and find that they can select their gamepad for use after an hour of searching, have it enabled by default when plugged in. A second would be to have better default controls for the gamepad itself.
If I'm not mistaken, aren't the joypads enabled by default as long as they're plugged in before it's launched? It's been so long that I can't remember. I agree that having the options laid out in a more streamlined fashion would help newer players, but I wouldn't necessarily call the current system cryptic. I go to options, control options then setup joypad. It's not the worst way to setup a controller.
PC gamers walk in to games knowing that they need to do a little more work to tweak the game to make it just how they want it. It's sort of the nature of our hobby. It's obvious to laptop users that any fast-paced gaming with a track pad isn't ideal. Most people who own laptops expecting to game either play slower paced games or have bought a mouse or joypad to better meet the needs of faster paced games.
You can't keep passing SRB2 off as a Sonic game when it feels like the regular DOOM fps with sped up physics, it just doesn't work. People walk into this expecting Sonic and get hit in the face with lord-knows-what. So the best thing to do is make it as easy as possible to get acquainted with the controls the easy way: using the tools they're likely to walk in with, and easing them later on into the game's style; NOT just saying "it's not professional so not everyone will like it".
I still stand by saying if someone doesn't like it, they won't.
SRB2 is built off of Doom legacy. It's still essentially going to be Doom, any way you slice it. What has been done with SRB2 is an impressive showcase of something I'm sure most people didn't even think the Doom engine was capable of. Rewriting core elements of the engine, such as its way of handling physics and input, is something that is very time consuming.
In essence, it
is Doom with different physics. Not to undermine anyone's efforts, mind you. Another phrase that quickly comes to mind is, "it's not professional, it's a fan game." The developers for SRB2 aren't getting any funding for their time spent working on it. We all have our daily lives to attend to, and while we all hold a special place in our hearts for our hobbies, they're still hobbies. I'm not saying this as an excuse for laziness, either.
New players shouldn't even SEE the options screen so frequently (not to mention most of the useless actions there that won't help them until they learn what most of the multiplayer stuff is and how it works helps at all), they should be able to jump right in with actual polish. This is what the game fails to get right for introducing people, and no amount of tweaking Green Flower Zone's layout infinitely will help this.
I agree that the best games are ones where anyone can just pick it up and play. I also agree that, once again, a more streamlined options menu would be nice. A lot of options also offer a certain level of flexibility that most PC gamers lust after and many PC gamers will go to the options before ever starting a new game.
The problem lies solely with it's controls.
If you walk into SRB2 expecting something like Sonic Adventure, then yes. This could very well be the problem. The controls can be alienating, but it is an issue that we all seem to have overcome, so it's obviously not impossible.
If you're going to introduce someone to SRB2 and want them to like it, you should try to help them overcome their issues. Even if you try to help them and they still don't like it, you shouldn't take it personally.
Edit: I also wanted to give props to Hinote's post earlier. It's pretty much the best answer Eliwood could get.