As a relatively new player, I've managed to get all 3 roles up to level 3. I feel perfectly comfortable playing outside of novice matches, but I still like sticking to novice matches at times because it feels less likely to throw me into the deep end against a full coordinated team.
It still happens even there, but it's less prevalent.
As for what I'd like to see, I think that players with only one role above level 4 should keep access to novice matches, BUT should be unable to select the higher-leveled role in novice matches, AND should be warned about the limitation and which role is unavailable when trying to load into a novice match. I'd also like to see players limited to ONLY playing novice matches until they have at least one role at level 3, or two roles at level 2 (basically 2 levels earned, regardless of same or different roles gives you access to non-novice gameplay). It might not be enough to get you good at the game, but by that point, you should have at least a basic grounding in the controls and functionality of the game.
As mentioned, I'm still a recent arrival. Even on my first day playing, less than 2 weeks ago, I was running into friendly faces in novice matches who were quite willing to offer helpful advice. Most of these players had only been playing a few weeks themselves, but as they had more experience than me, they had more of a feel for the game. It was pretty rare for information I heard in-game to contradict the established rules defined by regulars on the forums here - having read the forum and almost every page on the main site, I had as solid a grounding as I could without having the actual experience of playing - often things feel different from how the numbers and words line up.
If the experience I got as a new person is anything like the "average" new player experience, this game is actually one of the more welcoming online games I've played. That's not to say it's perfect (obviously), but Muse have got more right than they've done wrong, and I'm impressed by it.