When I think about supernatural shows, most of them had a way of either getting them out of the picture after so long or finding a way for them to interact with the other characters.
I remember one of the most blatant was My Hero, when their baby turned out to be a talking super baby. Damn, some of the stuff I used to watch
But other shows did similar things:
Being Human had one season with the baby being a main part of the story. They flashed forward to her future adult self throughout and ended the season killing her off.
Charmed also brought in future versions of the kids and did a season arc centered around time travel/alternate dimensions right after the baby was introduced.
Could even count Dawn really. Bring in a child for Buffy to look after, but have a reason for her to be a teenager right away.
A few other shows I can think of did time jumps between seasons so the kids were old enough to play a role (Ghost Whisperer for example)
So yeah, I can totally understood why they did it in AtS. Baby stuff just wouldn't fit into the series long term in my opinion.