I commuted wearing a backpack for a year. That was enough for me, but it wouldn’t have been as big a deal if it were like 5 miles or less I think. I’d never have been on the bike long enough to sweat much and it would have meant not less strain on my body but for shorter amounts of time. For me, it was cumulative and now I have lower back pain where there was none before.

Edit: the grocery store is 2 miles from home. If I needed to grab 3 bags of stuff and had a hiking backpack to do it with - hell yes that’s how I’d do it. But I’d only use it for short occasional trips like that.