Back when I used to dye my own hair, I found capes to be more trouble than they're worth. They never fit right and always left gaps where dye could drip through. A cheap old button-up shirt worked much better because it covered everything without slipping. Plus, capes are just one more thing to wash and store. I've had fewer stains using simple clothes I already own.
Yeah but a good cape has that snap closure at the neck, @michael_lopez53, which seals way better than any shirt collar. That gap you mentioned usually means the cape was cheap or put on wrong. Once you get a decent one that fits, it's way less hassle than ruining your own clothes.
I get what you mean about the snap closure, but honestly @michael_lopez53 has a point about the gaps. I tried a cape with a snap for cutting my dog's hair and it still got fur all over my shirt collar. My fix was just using an old zip-up hoodie backwards, it seals at the neck and covers my arms completely.