Blind pick is also a thing, but draft and blind share mmr, so it wouldn't really work.
Also, role swapping at the time of champ select is sometimes a thing, which could really throw off intended matchmaking. (Particularly where people in a premade could intentionally try to get their 'weak' roles in order to swap with their mates for an easy game.)
Also also, the meta roles aren't necessarily even things that every game will have, so people doing more creative stuff (duo jg, two supports, whatever) would have unclear mmr assignments.
Your best bet is to just bite the bullet and play your off roles/champs in norms for a bit until you learn the role better and/or fall to an mmr appropriate to your skill in that role, and potentially reserve your main stuff for playing ranked. The difference between silver and bronze isn't that huge relatively speaking, so it's not that big a deal to climb back up if you wanted though.
If your skill gap between roles gets really huge so adjusting your mmr is impractical, theres also the potential to whip up a smurf that specifically plays whatever role(s). That said, there is a lot of role independent game skill (overall macro sense and positioning and so on), so sometimes your skill level in roles you don't play might actually be higher than you think. You raw mechanics in whatever role might be say bronze, but if you had gold game sense, then you might find you actually do fine at a silver level once you actually get in there, despite lacking confidence to due the missing mechanics.