We don't do barrels. The reason we start slow is for the horse to get an idea of what we do. It also helps the rider who is new (as I was at the time) get in the habit of how to do things safely. I didn't canter the weave until I felt confident enough to actually do so. From there, at the points where it mattered, like my timing, I knew what I was doing and I trusted my horse to know what he was doing also.
Obviously horses aren't mindless drones. I know that very well. I made a mistake and I learned my lesson.
My apologies for giving an experience that wasn't directly related to barrels. Maybe I will learn to keep my mouth shut next time.
The really nice thing about slow work and doing it properly is when you do start asking for speed and the pattern falls apart, you can simply go back correct it and move on again. Everyone is different with what they choose to do, but I personally only work the pattern once a week maybe twice but not likely. The rest of the week it is flat work mixed in with drills and such.