While staying with my mother several times last year, before she went into a care home, I used my rucksack when walking to and from the supermarket for her - about a mile each way.
It worked very well for me, and i was definitely able to carry a heavier load that way than I could in carrier bags, though I appreciate that not everyone could do that for various reasons.
In fact I was still able to carry a bag as well, in which I put the lighter things.
In that area, a trolley wouldn't have worked well at all, as apart from half of the route including steep hills, the pavements were in a poor condition, and im sure the wheels on a trolley would have kept catching on the broken-up parts and possibly tipped it over too.