We've always had kids at funerals, mainly because they've been family funerals.
When my DBro died, his funeral was attended by about 250 mourners, friends/family, people, like me, DH and DS1 were in the UK from overseas. DS1 was only 9 months at the time, I don't think it occurred to me to leave him, not least because anyone we could have left him with was at the funeral!
As it was my DMIL flew down from Edinburgh and looked after DS1 during the service so I could concentrate on my parents and sister-in-law. But my 7 year old DNiece was also there and she was very close to DBro. I think we come at it from a "more the merrier" view of mourning and gathering in our family. And God bless for my niece and baby boy, they lightened the darkest of days.
That being said, I wouldn't want to attend the funeral of a friend or acquaintance with my child, from the point of view that I would think my attendance is to support the family of the deceased, show my respects and remember them, none of which I'd be able to do effectively with my child in tow.
But if the primary mourners wanted babies and children in attendance then I would happily bring them. Anything to help them really.