Like the title says, I think that STF, or skip the fun characters should be able to freely transfer their inventory. So that you don't have to buy the same item twice, not care about gold transfers, and so that it is more friendly to newer players.
One example could be, If people sent gold to their STF to buy a specific item-set (which generally people don't calculate to know exactly how much to send) and get back the excess carelessly. I think that this would also benefit newer plays so they are not staring at the 30K(exaggeration) gold they can't get back because they thought they needed more than they actually did.
I know think that the transfer restrictions are due to the gold that the STF gets and people don't just exploit the gold out of STF characters. Which is only 15,000. A very small amount that generally will not help people get the items they want on their STF. Simply remove the starting gold on an STF so that people could carelessly transfer their items to and from their STF's.