It would be very difficult to put a percentage on it because it is impossible to know.
I even tell my CCW students, they will likely fall into one of three categories. The first is people like me, you carry pretty much all the time, everywhere you are legally allowed to. (Which, in Utah, is more than pretty much any other state.) The second is people who just like to have the permit in case they want to carry somewhere. (This is probably the biggest percentage.) Then there are people who got it because it sounded fun and novel, and when they actually get the card, and carry a few places, They realize that it isn't very comfortable (mostly because they are unwilling to spend and try out the gear they need to make it work,) and just stop doing it. They let their permit lapse.
This is why I don't think going Constitutional Carry will matter very much. Utah has been shall-issue for 20 years. Those of us who are serious about it have been doing it and will continue to do it. People who just have casual interest won't keep it up either way.
As for how much you SHOULD carry: Hey man, it's a (mostly) free country. Do what you want. It's your keister. You aren't a cop, if you don't feel like it, you're having a bad day, your head isn't in it, you can leave it home. But remember, going back to the seatbelt analogy, we wear seatbelts all the time because we don't know when and where something bad is going to happen. It makes no more sense to not carry because you are just going out for a minute, than it does do not put on your seatbelt because you are just running to the store. If you KNOW you are going someplace that might be dangerous than normal, the correct answer is not to put a gun on and go anyway, the correct answer is to NOT GO THERE in the first place.