Me and most nearly everybody that I knew growing up did so. We were after as many as we could get, and grey squirrels are hard to get anywhere close to still, and in the open. miles
I use a .22 for most squirrel hunting, but there are times of the year, when foliage is very heavy, that a shotgun is more efficient.
Also a good solution if you're floating a river and mixing a little early season squirrel with fishing. Although only the guy in front of the canoe gets to shoot!