When I had DS1 (14 years ago), my parents looked after him while I worked. They were younger and fitter then and they were honestly happy to do it. If they hadn't, then I'd have been unable to work. I trusted my mum to look after him and didn't tell her what to do. Our ideas are much the same, but at that point she knew far more about babies than I did! She would have been offended to be paid for helping me. I come from a family where we all help each other out when necessary. I have helped my parents when they needed it, so it's not a one way street.
I think part of the problem is that both parents often need to work just to pay the bills. Cost of childcare is often prohibitive, so if the GP's don't step in, the family are up shit creek financially. Not everyone is working just to pay for luxuries, so are not taking advantage of GP's in the sense of getting free childcare and spending all their wages on holidays.
I have 4 children now and I know that if I had to go back to work, they would willingly step in again. However, they are older now and I'd be reluctant to have them do this. Four DC are very tiring. But it does make me happy to know that they would, if I needed it.
I know of GP's who've had the kids living with them mon-fri and only go 'home' at weekends. This has gone on for about 18 years. The GP's are knackered and have effectively become parents again, without anyone asking them if that's what they want. They are naturally very close to the kids, but it's selfish to have children and assume one's parents will be happy to raise them for you.