Suppressor hunting is really fun with a .22. My state allows it with no restrictions.
It's quiet on your ears.
No one else knows that you're hunting, which is advantageous.
It doesn't alarm the entire woods.
Some of the most accurate .22 ammo is subsonic, so you usually don't compromise accuracy.
In the case of squirrel hunting, surrounding squirrels in a big feeding area aren't nearly as alarmed (though they still scatter IME).
Sometimes you get a chance to reshoot if you miss, though that's more the case at ranges past 50yds. Honestly though, I've been able to do that with unsuppressed subsonic .22s at extreme range,too.
About the only cons are that you have to bring paperwork with you, and the POI change usually requires you to dedicate the rifle or pistol to suppressor hunting.
I'd like to try deer hunting with a suppressed pistol. My state allows use of easily suppressed pistol cartridges for deer, so it should be entertaining for an under 30yds stand hunt.