I don't know if anyone else has this problem, so bear with me :-)
Personally I hate having stones stuck in my tyres, it looks bad, makes an annoying sound, and I figure it can't be good for grip in heavy rain.
So I usually pry those little suckers ouf the tyre ASAP.
Lately I've been doing it using the parcel hook of a Victorinox swiss army knife.
Most of the stones don't go that deep, so the hook can sorta just get behind the stone and pull it out. It feels much safer and more controlled than using a screwdriver or simillar.
Just thought I'd share it, in case anyone has similar issues.