Is it strange that I wear a baseball cap everywhere so that I can use it as a purse in a pinch?
Why would you need to use your cap as a purse?
It has a lot of enough space for carrying my things
It's good to have a way to keep small items organized, but it's not right to rely on a tool that wasn't designed for that specific purpose.  I would recommend that you get your own bag to use for carrying things, and that way, you can wear your hat at the same time.
I just want to be expert at carrying things.
Well, a great option for you would be to buy a tote bag, or you may like using cargo pants. There are a variety of specialized items you can use for carrying things, rather than using a baseball cap which isn't as efficient.