I think that it will make the game too easy. It's a funny idea but I don't support it. The wise old man will check your bank for quest junk. That would be good enough!
At the time of the writing of this suggestion the WOM just looked at non-member F2P quest items. He has definitely been improved but still misses quite a few member quest items. That said I consider the quest related abilities of a Bank Adviser to be just a small part of the Advisers contribution to the game.