agree. I'm currently single and without kids, so it's not inconceivable that in my old age I might be in that position (although hopefully by then I will either have an AI robot to assist and drive me places!). Because of this I am taking steps now to ensure I will hopefully have alternatives - both financially making sure I have sufficient savings if I need to outsource care and investing in friendships where we can hopefully support one another if needed.
IF I got to a point where, for whatever reason, I didn't have friends or family who could help (i.e. they died before me, we lost contact, they were also in poor health and couldn't drive), I'd make arrangements like a taxi or patient transport.
IF none of these were suitable (e.g. I had to be discharged into someone's care) and I was so desperate a neighbour was my only option, I would firstly explain exactly why I was asking them, why I had no other options, and how much of a help it would be/how grateful I would be AND offer them equivalent compensation, i.e. pay them the amount an annual leave day would 'cost' them, plus petrol, plus a bit more in acknowledgment of the inconvenience, and then get them some nice flowers or a bottle of something after as a thanks.
If they still said no I would be a bit gutted, but ultimately have to accept it.
I wouldn't just make what is quite a cheeky request without offering anything in return.