Disclaimer; I'm just a gobber that likes big iron and not and should not be taken as the voice of experience.
I have a 25,000lb capacity Hyster and it needed tires for the front axle (4 tires). I started looking around for new tires, the higher price was a consideration against solids, but I went with inflatables because of the way the old solid tires failed. What happened is that they had separated from the rims allowing the tires to stay stationary when the rim was spinning so wearing the ID of the tire. I Was talking with a tire dealer and he mentioned that the tire probably failed that way because either someone was going from forward to reverse very quickly or trying to use the machine as a bulldozer.
So that got me thinking, the reason the tire separated from the rim was that the machine got stuck, and operator was trying to extricate himself.
Granted you could solve this problem (and it's been done by other in the past) by either driving wedges between the rim and tire, or welding flat "lugs" on the rim and then pressing the solids on so you've got more grip.
If I were running in a warehouse or in a good yard (haven't made one yet), the solids would have been ok, because the weight of the machine/load, you'd get some traction. But I'm not, so that's why I went with inflatables, better traction and I'm not going to worry about ruining a $1,000 tire because I got stuck.
Your experience may vary and I'm far from an expert.