More specifically, being restrained from frowning makes you less able to understand and process somebody else's anger or sadness. This is related to the claim that facial expressions can cause as well as reflect emotions.
This report says the results of botoxing the frown muscles are that the world seems less angry to you, so you end up happier, but on the other hand, if you don't understand another person's anger or sadness, you might react wrong.
And even if paralyzing your frown muscles can make you happier, that has to be weighed against having less understanding of what people around you are thinking. It's sort of an induced autism. So while I can imagine it being useful for people who are overly sensitive, I suspect the disadvantage would outweigh the benefit in normal people.
I've never been very sympathetic to the facial feedback hypothesis. It just seems flaky and woo-woo to me. The studies are at best inconclusive.
This study seems well enough done to me, just from reading the Science Daily article on it. I hope somebody replicates or extends it.