Perhaps not all the time, but you should keep them in your bag while carrying them to and from the course.
Not only will this help keep your car clean, but shoe bags for golf act as a brilliant defender against damage, so should your shoes be thrown around as you’re driving from A to B or something be dropped on them, they will be safe.
However, like most items of clothing, golf shoes need to be allowed to breathe every once in a while to help keep the materials in top condition and to avoid the build-up of dampness or mould - something that can happen if they’re bagged up at the bottom of a wardrobe all day.
Overall, keeping them in the bag some, or even most of the time, is fine. Just make sure you don’t pack them away and forget about them if you’re not going to be playing for a while!