The elderly cycle all the time, especially since e-bikes went mainstream. Most elderly stop driving much earlier than they stop cycling.
> assuming she did have the stamina to bike groceries,
E-bikes are a thing.
> if she fell she would not recover.
People who have difficulty with balance, either due to age or medical issues use (e-)trikes, for some examples: https://senzup.nl/driewielfiets/nieuw/
There are very few people for who cycling is not possible; there are so many options to make it accessible for almost everyone. Here is an example for people in a wheelchair: https://www.roam.nl/runner-handbike-20/a3535 , it basically hooks up to their existing wheelchair and turns it into a hand-operated tricycle.
I don’t understand the point you’re trying to make. Because you can make up some edge case for whom cycling is not feasible the 99.999% for which it is shouldn’t either?