I don't know a lot about warehouse work, and most of it is second hand, but I don't think anyone works as hard as Amazon warehouse workers. Yes, having robots deliver stuff to you is more efficient, but it sounds more like Lucile Ball in the candy factory trying to keep up with the conveyor belt.

Generally the conveyor doesn't go faster when you get faster. The warehouse robots are just working on queuing theory. However fast you go, they'll just schedule more shit to come to you.