Remove Blind Pick
Only thing different between Blind and TB is that in TB you get the roll you want, you can leave the queue if it turns out you can't play. In blind, you have to call your roll which has a chance of being taken anyways by a troll. If Blind was removed queue times for TB would be much shorter and people would be less likely to rage quit because they didn't get what they wanted.
EDIT: Thanks for feedback guys Firstly, "Like others said, sometimes if you cannot decide what role or champion, go into blind pick and hit random." In blind you can't just hit random, especially when you get a group of people who don't want to break meta. IMO random should be available in TB and it if it was it would be much better than in blind because once you have your champion you can queue up in that role (sorry, couldn't figure out how to quote it lol). Secondly, if the amount of players who played Blind went to TB queue times would be just as long as blind if you stuck to meta, if not only a minute or so longer. The only reason why TB takes so long now is that there aren't too many players queueing and every time they queue they get matched with people nearest to their skill level while also factoring in whether or not they have played the champ, lane, etc.
Thirdly, new players could easily get used to TB, in fact they would probably enjoy it. Something I think would be a cool addition to TB is a TC could choose a specific champion and role and whenever you go to queue up, it would show you "Hey, people are looking for Nasus top right now", giving new players a little more incentive to try new champions.
Fourth(ly?), Of course, this change couldn't be implemented with TB in its current form, I think giving it some more options when queuing to draw a larger player base beforehand would be great.