Game consoles were (and still are to a some degree), by and large, toys. Toys that parents buy for their children with the expectation that they can be mostly left to their own devices with them. The ESRB/PEGI/etc. ratings system was put in place so that parents would be able to trust that they know what's in the toy without having to sit over the kids' shoulders every single minute they are playing. In a sense it's not unlike Mattel spending a lot of energy making sure their dolls and action figures don't pose any choking hazards.
Allowing modding breaks that system, and by extension the accompanying trust. This is a big deal for a toy manufacturer. It's also why Hot Coffee was such a mess despite the content not being normally accessible. Parents don't want to have to care about technicalities.
People like to think of this situation as a "think of the children"-type of hand-wringing, but it's actually more of a "think of the parents", who happen to be the ones with money.
Again, not discounting the greed and DRM aspects of this, and it definitely sucks pretty hard for adult users of the systems, but it's far from all there is to it.