Plenty of Europeans have cargo bikes and make do with 2-3 supermarket trips per week for families of 4-5 peeps.
Only bulk drinks (crates of beer/soda/...) are challenging. But for those, very often delivery systems are in place that surely are more efficient than individual trips anyways.
I regularly carry four cases of water (48 cans) on my standard bicycle without a problem.
Whenever I go grocery shopping I mount a milk crate to my rear rack (this takes about six seconds) and put the cases in vertically. I can also carry a 4L jug of milk in the handlebar-mounted basket.
Only bulk drinks (crates of beer/soda/...) are challenging. But for those, very often delivery systems are in place that surely are more efficient than individual trips anyways.