I do think it's a nice idea, and far better than a lot of other ways of behaving. But really, doesn't giving one to everyone, mean that just having one doesn't make you special? Then the people who have two are special. I'm just not sure how I'd feel about getting a "pity flower."
It might be one of those situations where there's no good solution. If you allow people to get different amounts, it becomes a very visible popularity contest. But if everyone gets one, then no one is special, and the whole thing is kind of meaningless and generic. And if you don't allow any, people get upset that they can't celebrate.
In an office of adults it's usually the first response, and you're supposed to be mature enough to handle the visual as long as people aren't rudely rubbing it in. But with kids I think that can be a lot to ask.