Bleedin'
It's not a big deal doing a slab after a shed is up, and you would never ever pull a shed down just so you could have the slab underneath it will be sitting on footings and is not worth the effort. Early on the bulk of sheds where probably done that way in some areas. The bull float is easy to use from an open garage front, and with a screed and a couple of cheese boards the slab is a bit of a doddle except in winter when drying becomes a pain. Depending on how good a finish you want I wouldn't sway a weekender from it other than to say it is a bit harder than it looks and worth employing a concretor to help on the day.
There is absolutely nothing wrong with the construction technique and after all this is an old shed getting a new floor so lets not get to excited about the whole job.
John