Why don't you get someone to carry you to whatever rank you think you deserve (or higher) and then get outplayed until your LP/MMR/Rank falls back down to bronze?
That way, you'll know it's where you belong.
Joking aside though, a test does seem like a legitimate way to better prepare people for rank. But I think it should come into the form of an advanced tutorial, that explains and shows you specific tactics that can be used generally for that role, and then makes you perform that strategy or hit a certain benchmark under pressure of time and an enemy AI presence, all relative of the skill it's trying to teach for the role you're playing. The skills it would teach would be general skills, not champion-specific ones, like freezing a lane, forcing the lane to push to you, having a certain CS in a certain amount of time. These tutorials could unlock at level 30 and then you couldn't unlock rank until you completed the advanced tutorials.
Not saying it's the only solution, but it's an acceptable one right? People will complain about having to go through it multiple times because of their smurf account, but once it's done, you never have to do them again.