Possible fix for the "Mastery lock/Trade" problem?

Instead of having people trade Champions.... Why not trade positions in pick order?

People already say "Hey man since your first pick, want me to top, or trade for you since im support last pick?"

So why not... Just change the pick order? Let it be random, if people can agree on trading spots so top/mid can pick last and adc/supp/jungle can pick first, second, or whatever they want to do, they can, as thats the goal of trading anyway.

This way, you can just trade your order, after ban phase, or even before (and keep bans if 5th went to first?). Then pick whatever champion you have Mastery 3+ for.

Any problems?