I suspect that most people (or at least those of us who have a whole bunch of bags) have some system of keeping their bags organized so that they can find what they're looking for. The game actively works against this when adding new items to your inventory: they're always put in the first available open spot, either in your main inventory or in the first available bag with an empty spot. Some people get around this by putting an empty bag in the first slot so that it'll catch new things, but that still leaves players in the position to have to go and manually distribute its contents to other bags when it starts to get full.
I'd like to see the game make some better guesses as to where to put things, based on what's already in your inventory. I can see two ways to do this:
1. If there's no room in the main inventory, attempt to place the item in whichever bag is open, rather than whichever bag is furthest to the left. This would mean that if I'm mining, I can open up my mining bag and have new rocks land in it automatically, and then later when I'm harvesting trees, I can open up my cherries-and-beans bag and have them go there.
2. Attempt to place the item in a bag where similar items already exist. This mean that if I have a full stack of beans and then I harvest more beans, the game would put the new ones in the same bag as the existing ones.
I'm sure there are additional possibilities as well, and I know that no solution would be a perfect fit for everyone's style of keeping their stuff organized. Regardless, it seems like almost anything would be more useful than the current behavior.