I think you have a problem with germs.
Others here have pointed out that mixing, say, meat and bread can be bad, if the packaging on the meat tears. It's also been demonstrated that if the reusable bags aren't properly cared for (which most people don't do, due to some combination of laziness and business), they are giant germ factories. Not so with single-use plastic (which I then re-use at home for mini-trash cans, bagging up loose recyclables, etc.)
I don't buy much when I go to the store, so I'd find lugging around reusables a pain -- I usually just use a hand-basket (I buy most of my heavy stuff in bulk separately from my weekly grocery run), so then I'm either stuck carrying a basket and a bunch of bags (since I usually need 2-3 bags to separate things) or having to use a cart (significantly slower to navigate the store) so there's enough carrying space to comfortably and conveniently fit both the bags and my groceries.
If it's 100+ trips to balance out, I only really go once a week with a few extra trips mixed in. And since I'd need 3 such bags, that's 300+ trips or about 5 years which hardly seems worth it to me for that level of inconvenience. Better solution? Bag in reusables, but be able to bring them back to a drop-off point at the front of the store like the can/coin machines. You drop the bags back off, the machine weighs them, you get a coupon for $0.25 off per bag returned (or whatever the rate would be) and the store then collects the bags, washes and decontaminates them in bulk, and the cycle begins anew. The obvious problem here is people overusing bags to get a bigger discount, but I guess you could only do this with the non-self-checkout lines where the store is bagging. Or you could make it something small like a penny per bag if you scan your store rewards card (although then people might hoard 200 bags).