Speaking only for myself, a large haul like this happens maybe once a month. I usually buy for more than the week (or the next one), so a large bag of rice, for example, will last quite a while but will take up room/weight for that grocery run.

For grocery runs in-between the large hauls, which are mostly perishable goods, I can often get by with just a single pannier, or maybe two if I'm getting something that takes up more volume.

The less often I'm in a store, the less I tend to spend throughout the month, so it's a strategy I use to keep my grocery budget in check.