If you've ever watched a horse race, you'll see that the jockeys are basically tossed into the saddle as the horse walks past (This becomes frustrating when retraining racehorses).
There are two reasons why they do this:
1. Speed. Basically, they're putting ten or twelve jockeys up in a limited period of time. Stopping each horse and carefully legging the jockey up takes longer.
2. It's actually easier on the horse. We make horses stand to be mounted for our comfort, not theirs. (And safety, especially in the case of less experienced riders). Racehorses are young horses that are still growing and don't need any extra strain on their back, so they're mounted at the walk, when they can compensate for the jockey's sudden arrival by moving forward.