Thanks for the nice comments about the bags I made!
If I'm shooting for fun or at a woodswalk, I use a ball bag of any type and there's no rush or pain or problem. Nobody moves quick at those types of events and the pace is usually pretty slow. If I wasn't too busy or lazy the night before maybe I'll take the time to load a larger ball block.
If I'm deer hunting, I use a smaller ball pouch that maybe holds 10 balls max, or a little ball block. I also keep a few lose balls rolling around too or in a small pocket inside the pouch if there is one.
I haven't encountered every situation possible by any means, but in my limited experience so far, if a deer is bewildered enough after being shot at (and maybe even hit, has happened to me) and not panicked and is sticking around to give me a second shot, then it doesn't matter where you get another ball from as long as you do it in a hurry but take your time. In other words, if the deer isn't running like $#*!...no need to panic, you'll get a ball out of a pouch, a block, or even the bottom of your bag in plenty of time. I've even rolled out a ball from a pouch, put the stopper back in, cut and greased a patch, loaded, and shot again while one was blinking around after being shot at.
If I'm hunting with shot, and I really want a fast second shot because the dog might kick up another pheasant or rabbit, I stick with paper cartridges. Otherwise it seems like there's too much stuff to fumble with for fast moving small game with wings or fast feet. I've been slow-loading with shot in a pouch or bottle and loose wads/cards for squirrels with no problem as of yet, but I want as dense a pattern as possible for them also and can't get that from a paper cartridge.