I can’t speak for everyone, but my sense is that the primary difference is due to relationship. For many women, they have a closer relationship with their own mother than MIL, so it simply makes sense that when you’re feeling most vulnerable and emotionally raw, you’d turn to the person closer to you. If there’s EVER a time to put your own feelings and comfort first, it’s labour/delivery/post partum!
I think it’s probably unusual that someone has as close (or closer) a relationship with in-laws as their own parents.
It’s fairly easy to solve, though. Husband hosts his parents when available, Wife hosts hers. Anything more should be viewed as bonus vs expected.
I think expecting a DIL to treat her MIL exactly as she does her own mother is probably where a lot of issues stem from. The relationship simply isn’t the same for most people. Weirdly, I’ve never seen anyone complain that a SIL doesn’t treat his MIL like his own mother.
And the relationship pre-baby isn’t magically going to be closer after. I’ll never understand parents/in-laws/extended family who saw the couple a few times a year pre pregnancy expecting to reside up their nose after baby arrives.