Oh, that's cool. It's an effect you want sometimes. eg. if you have a combo deck that relies on searching out a key piece, if you have excess land and want to shuffle your library, if you want to keep a card in library and not graveyard if opponent has a discard spell. And is a defence against decking yourself.

And yet, most of the time, there's no particular reason for it so there's no danger in letting you do it multiple times. (Or is it broken in some way I haven't spotted?)

I don't think so, but I'm often pretty bad at spotting that.

Wizards wouldn't print it, because they're trying to cut down on shuffling (because it's time-consuming busywork), but from a theoretical or MTGO point of view, I can't see any problems.

Maybe "on the bottom of your library" would work equally well?

What Wizards really doesn't like is making your opponent shuffle, which is why Myr Mindservant only effects you. If you want to keep shuffling your library, Wizards tolerates that.

Bottom of library would probably work just as well. I don't think it opens up any combos that shuffling doesn't.