Well I guess this forum is a bust...

Probably not, but I'll bet your doors are actually hollow core. Hence the reason they sound and feel hollow. You could fill it full of fiberglass insulation, but filling it full of spray foam would just increase the cost and aggravation when it comes time to replace them. And more than likely, the spray foam will push on the jambs, making the doors hard or impossible to shut/open.

There should be shims or blocking at a couple of points between the frame and the studs, most importantly at the point where the lock strike is on one side and at the hinges not eh other. The rest his typically left open. Your issue is more likely the doors themselves, as noted probably hollow core. Replacing the door slabs will probably accomplish much more than anything you do to the frame.

If you can fit a 2x4 in the shim space, thats a pretty big gap I agree. Usually a rough opening is 2" larger than the door size and the jambs take up 1-1/2" of that space leaving 1/2" left. That would allow for 1/4" shim space on each side.

If you want to sound proof the shim space, you would be better off with wool or denim insulation than spray foam. Sound is stopped by dense items, spray foam is not very dense. That being said, as recommended you should change the doors to solid core instead of hollow core as well

If for some reason you feel you must spray foam (even though you shouldnt because it will be a pain for anyone adjusting the door in the future), use latex non expanding foam (DAP Dapdex) otherwise you will ruin your door (aka it wont close or open properly). The latex foam is also easier to remove in the future if needed.