Well exactly. My DH was thinking of offering to regularly mow the lawn of our new neighbour (female 40s,) as her lawn was getting high, and she couldn't seem to keep on top of it. He also said I could offer to take the woman across the roads kids to nursery when her workplace wanted her to start at 8.30am instead of 9am. 
He also said I could offer to weed and trim and neaten the garden of the elderly lady 2 doors up who was struggling to find a gardener. (He knows I enjoy my garden, but I am not doing anyone else's!)
I said 'fuck that for a game of soldiers' to all 3 suggestions. I will help anyone in an emergency, but I am NOT going to offer to be anyone's 'regular help.' No. WAY. And neither are YOU!'
I have mentioned this before, but basically some years ago when my 2 DC were infant school age, I used to visit an elderly great aunt. (My Grandad's brother's wife. Grandad's brother died in the early 1990s.) No-one in the family could be arsed with her except me, including her own 2 middle aged adult sons who lived 30-ish miles away...) I would take her cakes and magazines and sit with her for hours. (I visited twice a month, sometimes with the DC, sometimes just me.)
She went into hospital for a big op, and was in there for 3 weeks. I visited 6 or 7 times. (I lived 20-25 miles away.) A few days before she was due to be released, the Staff Nurse cornered me, and basically told me she needs to be picked up at midday on Friday, and will need full time care for 2-3 months, and hopes she can have her own room at my house.
I said 'whaaaa?' and was aghast. They were expecting her to come live with me! I said 'I can't look after her. I have 2 small children, I have a job, and I have just 2 bedrooms. I can't look after her. What about her 2 sons?' The Nurse said 'they are very busy men, far too busy with careers, and they're men. You're a woman, and a mum, so of course we're looking to you.'
Long story short, I put my foot down and said 'no way.' The nurse looked disgusted with me and walked off... My great aunt never spoke to me again. She put the phone down any time I rang her. I tried half a dozen times before giving up. I don't know what the nurse said to her, but she disowned me. It was a case of 'no good deed goes unpunished.'
But yeah tr;dr because I had shown a degree of interest and caring, it was assumed I would take her in and be her carer! A 30-something young mother with 2 small children, a small home, and a job! AND my own pension age parents who I was already doing stuff for. (Some housework and bits of garden help, and shopping! And running them around now and again.) Also, where the fuck would she even have slept? And what about my children? They were still small, and young, and needed me.
Bloody ludicrous. And this was over 20 years ago. I could imagine it being the same now, even if it was just a neighbour. My relationship to this great aunt was not close kin. She was not even a blood relative. She was my great uncle's wife who he had been married to for 15 years before he died. (The father of her 2 sons had died some years before when the boys were young adults.) Yet the hospital was trying to shove her care on me, and have me take her to live with me and my family!