No, they shouldnt be able to trade at all. for obvious and game breaking reasons.
The same goes for keeping your gold and items when you re-stat.
Why would anyone play the normal way, and level up, if you could just keep everything on a character that took you ZERO effort to accumulate any wealth and put you at the top of the pile stat-wise.
NO
The whole reason you STF characters are gimped is because of the rewards system currently in place for people playing cRPG. yes, cRPG. the STF characters arent playing cRPG. They are plaing like native players with the difference that they have control of their stats. As it is, I think you are lucky enough that you can acumulate gold and items on an STF char that you did nothing to earn. You already start with 9,900 more gold than a standard cRPG player, how much more do you need the system to hold your hand?