Insulation foam is stiff and will not flex. It will permanently deform as oldE already pointed out.
Watching that video, I was wondering if that guy was serious? Especially when he showed the tire he "overfilled".
There is a reason people have come up with this air cushion (and it remains until today). Maybe yard equipment doesn't need that much cushioning, but I'd at least try to use a flexible foam. They may be available, albeit not as readily as insulation foam.
I would consider switching to full rubber wheels on something that got on my nerves in the yard instead.
G