It’s not my experience, at all. I also think it depends on how you define help and support. In the early days mum and dad often need different things. Any emotional support my dil may have needed, came mainly from being hormonal, sore, exhausted from breastfeeding and, (once his 2 weeks paternity leave had finished) alone with the baby for 12+ hours when my son was at work. These factors just didn’t apply to my son. It wasn’t that he wasn’t ‘worthy’ of support, he simply didn’t need it.
My dil has always said that the thing she appreciated most in the those first few weeks was adult company. My son was out of the house for over 12 hours, she was alone. She and I were close before she had dgs, so I used to pop round for an hour or so, have a cuppa with dil. That was only ‘possible’ because we had an easy relationship. Quite often dgs would be asleep or feeding the whole time I was there. It would have been a very uncomfortable 90 minutes if dil hadn’t got on well. Where that been the case, I can understand why mil isn’t the one dil ‘chooses’ for company. My son simply didn’t have the same ’need’ for adult conversation/company. He was getting it at work.
As far as ‘help’ goes, I’m not sure what you mean? When it came to dropping round food, making a cup of tea etc all help was appreciated and accepted equally. If you mean specific baby care, my son and dil didn’t ask or seem to require any help. I (and I’m assuming others) occasionally ‘watched’ gs for 10 minutes while dil had a quick shower. But son and dil were both capable and keen to take the lead with their own child. I think sometimes as grandparents we underestimate our adult children’s ability, and overestimate their reliance on us.
As my gs got older, I saw him most, simply because I was the only retired grandparent. This was largely facilitated by my dil, who invited me to spend time with her and dgs. My own son is very protective of his family time, and if left to him, I’d see my gs a lot less.