It's difficult to play WELL at a fast tempo, but it's easy to play too fast as long as you're OK with not playing very well at all.

Practicing slowly ~ "too" slowly ~ forces one to pay more careful attention to the subtlest detail You have to be extra-careful with timing, pitch, and everything else when proceding at a super-slowed-down tempo. Ideally, you will then take what you learned with you when you go back to playing the piece at an appropriate (quicker) tempo.

But not TOO fast, of course!

I'm getting into choral singing fairly seriously these days, and have been learning first-hand how much I'm able to learn by practicing at a "too-slow" tempo. And, aside from applying this new knowledge to singing with the group, I am also finding that this approach works just as well for my guitar-playing.