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You only need one bag, so it’s not a burden at all. Worst case, it’s incredibly easy to add a basket to a bike (or mobility scooter), so you can put your day’s groceries in there.
And as an added benefit of density, grocery stores are more efficient. There is a “general” one with all of the basics — fruit and veggies, cereal, meat, pasta, basic sauces, breads, convenience foods. Those are everywhere. Then if you go a little further, you’ll find specialty stores with “asian foods” or others, which you may not use as often but can get some rarer things there.
In the Netherlands you'll see Bakfiets/cargo bikes. https://www.bakfiets.com/
Every few weeks, we load up the car with all of the non-perishables, at a huge discount supermarket that's a few miles away.
Seems like an OK compromise.