If you bar players from taking a shot in the shootout if they are in the penalty box, you may open a whole can of worms with intentional penalties.
For example, say we're playing the Leafs. With 1 second to go, someone who can't shoot well (pick anyone on the Leafs) shoots it over the boards and gets a delay of game penalty. Wade Belak jumps on Alex Kovalev and punches him outright. Kovalev doesn't retaliate, but Markov does and so does Komisarek. Hapless Leafs jump in (though none of their shooters).
Multiple roughing penalties get handed out: 5 to the Leafs and 2 to the Canadiens. Notably, the Leafs lose none of their successful shooters, but manage to shorten their shooting bench to 15, so if the shootout goes beyond 15, Sundin is up when Gorges is shooting for the Habs. The Habs lose Markov who was goaded into a penalty.
Or take this example. I'm the Bruins playing the Sens in March. Gerber has been tanking now for a while. Andrew Alberts runs Emery and gets him to take a swipe. Both get penalties. Alberts can't shoot (who cares), and Emery must watch Gerber face the shooters.
This time it happened to be Gonchar that took the penalty, but more often than not it is not a skilled player doing that in OT (or any part of the game for that matter). Therefore, on average, between shortening the bench, targeting players to instigate and the chance of goalies missing the SO, there are many implicaations for this suggested rule change.
I wouldn't suggest asking for it. That is unless the Canadiens are craftier than I thought and have all these gameplans of their own up their sleeves.
Here's my proposed solution to the problem:
If the team on the PP scores on their first penalty shot, the game is over and won. No chance to reply for the offending team.
Wouldn't see many penalties that way, I bet. Whaddya think?