At its core, its not a to bad of an idea. However, your solution poses another problem.
The whole reason we don't queu up for the slot we want to play is because a good player understands the need for flexibility. For instance, during a ranked match we had all semi-decided our roles and I was going solo top. The opposite team, however, had picked a Skarner and a Tryndamere. This of course meant Tryndamere was going to end up laning up. So I asked if anyone could take Teemo top. Normally I don't promote Teemo top, but Teemo absolutely crushes Tryndamere and I did not have any solo top that would absolutely guarntee victory against Tryndamere like Teemo would. In that game, I switched with the jungler, our support went jungle, our ad went support then I ended up playing ad.
That probably wouldn't have been possible if we had pre-queued for a certain slot.
Also, I find it highly unlikely that in ALL your recent 5v5 games you encouner people who will only stick to one slot. I usually encounter them every one in four games. And almost a hundred percent of the time, whether or not they get the position they want, they feed. I don't think theres a way to make up for simply bad players who have little thought for team cohesion.
However, is you idea necessarily a bad one? No, of course not. In fact, it may very well work out incredibly. I can see this solving a lot of problems. But, I would restrict only to Blind pick considering you can't counter pick the other team and, of course, can't have your champion banned. I think this would work very well for Blind pick.