I hope this is possible with our new Client. It's something I hoped that would come along with its release.
Add a button next to every player on the spot of the 'swap champions' button, but in the previous phases of the draft. Click on the button of the player you want to swap positions with.
Swapping champions require both players to have each other's champions. This impedes tactical drafting in soloQ since you don't know which champions the other player has or wants to play. Some players like to first pick their power pick while others want last pick to counter.
Also, no more the occasional troll who promises to swap and then doesn't. Pure evil.
The only concern here is for Riot's wallet. I'm not sure how big of an impact this will have on the purchases of champions with RP, but I can imagine that less people would go for an instantly full champion pool. That being said, I believe that champion purchases is a tiny fraction of their income and most of these are probably players pre-level 30.