Roll up looks more sensible than a "bucket".
I bought a DeWalt bag with sewn in pockets for everything. It was fetching to look at. I thought, this could be my road bag when standing in Home Depot just before purchase.
Picture yourself digging into the center tub of stuff for that small container of plumbers putty you haven't used in nine months.
If I use it I pack it before each trip. It's not a good catch all.