This reminds me of the RAW arguments I've seen in the past:
Player: "Well RAW says I'm not encumbered if I'm carrying 150 lbs of something."
DM: "It doesn't matter, carrying 150 lbs of styrofoam will encumber you. It's too big to fit in your backpack and will require an acrobatics check to see if you can walk while balancing it on you. While you concentrate on keeping it aloft, you can't have weapons, move at your usual pace, or engage in combat without putting it down."
Basically, be realistic about it. Close your eyes and picture how you imagine your character looks. Where would you keep these pouches so you could fight in combat? How would they get in your way if you had 50 of them? Is this belt held up by a shoulder sash to accommodate the weight of all of these pouches and their contents?
This all boils down to roleplay with a generous helping of logical consideration. By RAW, you could carry a limitless amount. There's no hard number.