Executing fast is important, but practice slowly. It is frustrating as heck to admit it, but forcing your body to do something slowly is very effective at learning to do it at speed.
Slow is smooth and smooth is fast.
As the Romans said, festina lente.
I think ideally you need to practice both slow AND fast. You need to practice slow so you can notice and work on small details that can be skipped over with speed, and you need to practice fast because some things are legitimately different at speed and you won't learn how to deal with them only going slow.