I feed straight alfalfa almost all the time because grass hay is outrageously expensive here (I'm in Arizona). I mean, I can be paying $9 for alfalfa, and bermuda, which is about the only grass hay you can get regularly, will probably be about $12-$14 a bale.
Sometimes the feed stores get what they call a grass/alfalfa mix, but almost always it is some mystery grass and there are plastic bottles and cardboard boxes and such baled in with it. I think they are charging you a premium for what has been growing on the edge of the field near the roadway and calling it a grass/alfalfa mix! So, I basically have to feed straight alfalfa unless I get really lucky and find some nice grass hay to feed with it.
I have neighbors that swear it gives their horses too much energy, but I ride my guys regularly and don't notice or mind. I'm really not sure if it gives them more energy or not. I am a big believer in riding my horses, and I notice that horses that don't get ridden regularly have tons of energy no matter what they are fed!
You don't need to feed as much as grass hay. They usually break off in pretty nice flakes and I just feed a flake morning and evening (these are 3-wire bale flakes, not 2-wire bale sized flakes).
A lot of people don't think straight alfalfa is healthy because of the excess protein and calcium, but a lot of us Arizona folks feed nothing but alfalfa year round (because most of us don't have pasture either) and the horses seem to do just fine. In an ideal world, I would feed about 50/50 grass alfalfa.
As for health benefits, I would say less hay-belly because you are feeding less to get the same results, nice hair coat, etc. I think there is also a study that says that the calcium in alfalfa helps keep horses from getting ulcers, or at least buffers the stomach acid a bit.
Potential negatives....I have heard that horses are more likely to get entroliths when fed a straight alfalfa diet. I don't know how much of an increased risk there is though.
I have lost two horses to colic, but they were ages 24 and 26 when they died (not that it makes it any easier to loose them). And they were not necropsyed so I don't know what went wrong with them. So I don't know if they had entroliths or a twisted gut or a bad impaction or some other problem due to their age. They were also Arabians, whom I understand may be at more risk for entroliths.
But I am still very comfortable feeding alfalfa. And if you feed at least 50% grass with it, I really think it will do your horse good and have no ill effects like a straight alfalfa diet may (or may not) have.