Yes, you can bring a bag. Personally, I am happiest when I don't have one, or have only a tiny crossbody bag.
In some seasons/weather, we are forced to carry extra water and/or jackets of some kind- so then we end up with a (bigger) bag.
I have done almost every kind of bag at WDW (except I refuse to ever do a fanny pack). The thing with backpacks is that they can be a tricky fit on a few rides (SM), I also don't like the feeling of having something wrapped around my legs, or having a sweaty back under the bag, or that tired feeling of carrying a big weight all day. If you can limit yourself to a tiny crossbody bag- then you don't have to do anything with it. It just hangs at your side all day, and stays put on rides. Using the pouches is an easy way to leave something behind (been there).
Another solution is cargo shorts. Men's cargo shorts are especially good for carrying things. Jacket pockets can also be used.
A big plus for eliminating the bag is that you get to bypass the bag check.
If we must bring a bag, I also personally try to limit my bag to one compartment, which is easier at bag check. A pet peeve of mine is getting stuck behind a clueless guest with 20 pockets and no idea that they have to open all of them for security!
Oh, and if you plan to go on Kali- sometimes a waterproof Ziploc bag is a plus for expensive things.