We live in an dairy barn with a HUGE hay loft, and I would vote no.
Fire is always an issue, whether hay is wet or dry.
The advice to "never bale wet hay" is great for folks with experience.
Most homesteaders are learning. "Dry enough" is not an exact science.
There may come a time when you have to buy hay on occasion.
You can never know what someone else has done.
Dust and mildew are a problem... We have a very airy loft. The prevailing wind tunnels through, but coughing and allergies still come up when we work up there.
The heavy work load is a problem, too. Stacking hay is hard, dusty work.
If we could start over, we would build a dutch barn with great ventilation for hay only. We would have enough hay wagons to just drive them in there and park em.
No more unloading and restacking. When the baler kicks it in the wagon, we can stack it once and for all.
It would be far from the animals. I could lock them in the barn if I wanted to or needed to without worrying.
I could drive one well cured wagon load of hay at a time into the animal barn and still have convenience.
Insurance would not be an issue.
Dutch barns are CHeAper to build.
I love lofts. If you can afford it, build it and use it for something else.