Don't be daft. Nobody has ever said a MIL is overbearing for "wanting to hold a new baby" though some have been upset at their MIL charging through their front door and kissing their baby when asked not to, or bossing them around when it comes to feeding, or grabbing the baby and leaving the room when a new mother is lying there exhausted and teary. And etc.
Some do say their MIL is remote, they're generally told that an MIL can have any life they want.
The threads you see on here are unlikely to be "My MIL is great" because after all people are posting problems. Start a "My MIL is great thread" post all the things she does and see if people join in.
Though again, as this is basically an agony aunt site with thousands of wannabe agony aunts commenting, you probably won't get as much traction.
And contrary to popular fables, lots of MILs have great lives that just don't revolve much around what their grandchildren or dils are getting up to, and you're hardly going to hear from or about them.
As to the wider issue - the only area women have ever held any historical power - and not always then - is in child rearing/family units.
Women are constantly encouraged to compete with one another for any available attention and power, this is a society wide issue and has been encouraged by everything from "jokes" and movies to comments within families, so naturally when they see their tiny scrap of perceived power diminished some will react badly.
If you can keep women arguing and unhappy with one another they won't band together to try to change things like those annoying Suffragettes did. See Afghanistan right now, where women are enslaved and literally told they cannot even speak to each other. Women cooperating can be dangerous for the status quo.
So, it's in the status quo's favour to encourage women to attack other women and society does this in many ways.
And women are almost without exception an easier and weaker target than men, so many women will fight amongst themselves rather than trying to get their husbands/fathers/brothers to change or improve.
Lots of men enjoy watching their female relatives fight with one another, it amuses them and reinforces their backwards notions about women generally.
Men as a collective are often extremely aggressive to one another, but this is a site dominated by women so you won't hear as much about that.
And a lot of men don't care what women are doing to one another unless it affects them, so just leave them to it - meaning a woman has no back up from her husband/father/brothers and will write to sites like this instead to try to figure things out.
So, basically, there are many interwoven reasons why you will read about MILs behaving badly here. And none of them are "MIL wants to hold the baby".