Absolutely. I can’t imagine doing either of the setups you describe. I have a kid who has worked for me since he was 14 (now 18) - first job was mucking stalls at another barn and no matter what it was terrible. They had a tractor but it was muddy, and slippery, working around horses that couldn’t be turned out yet, etc. Just a nightmare.
I only ever saw one really good setup, and I’m sure it had all to do with having money. Two or 3 people worked together, sometimes 4. 1-2 picked stalls and put dirty bedding in the doorways, 1 person drove the gator with auto dump bed. The extra person just shoveled into the gator, whose driver would drive to the pile with a ramp, and dump from above. They also had an excavator to level the pile so it could be filled evenly.
I’d never seen stalls done so quickly. If they didn’t have extra people, they would still use the same method, just slower. Pick into the entry way, and pick it up with the gator. But also importantly, they had a system for turnout that unless that absolute worst weather, at least half the barn would be empty all at once to make this process easier.