At first I was going to say there's a lot of ignorant people posting in this thread, but I realized most of the people with snowboard hate are the same people with low post counts. A lot of people who are hating, are the same people who argue with "skiing is better because snowboarding is gay". In all reality, snowboarders will do just as good as job as any skier.
Boarders can't strap in as fast. Anyone who actually rides with good snowboarders, knows that it's a matter of seconds getting strapped in. And a lot of good boarders can strap in while moving away from the lift. They don't need to sit down to do it.
Boarders can't go in the bumps. As a boarder, I have no problems with the bumps. We're talking about trained patrolers here, not your average joey.
Boarders can't handle steeps. In all reality, boarders are better suited for the steeps. They can kneel down and dig their entire toe edge of their board into the snow, and still be able to work just fine. Skiers can either dig their boot toes in, and move around, or try and work with their skis still on.
In flat areas boarders would have to push. What's the difference between that and a skier skating? If you've ever seen the two, they'll move at close to the same speed.
Doing avy control. As far as moving around sideways or uphill, it's no different. It's not like skiers are gliding uphill. either way you're walking up hill, one caries their snowboard, one carries their skis. Moving sideways in deep snow isn't actually difficult on a board just skating. I'm sure it's not that more difficult than skis. You do have a valid point about stomping cornices, but if a boarder is assigned to that job, they'll have a shovel, collapsible pole, or something similar. Correct me if I'm wrong, but they don't get sent out as single persons to do this job. Odds are, a skier will be with to stomp a cornice if really need be.
Handling the toboggan. I don't see how this is an issue. There's no difference between boarders and skiers. Both are going down the hill, shoulders forward, toboggan behind them. Just because they're a snowboarder, doesn't mean they can't turn their torso. Both can turn just as well.
I think what a lot of people are forgetting, is that either way, boarder or skier, they're trained and skilled . We're not talking about you're average Texas joey here. They have to pass the same tests to be allowed to patrol.