I attend a lot of weddings - sometimes 2-3 per weekend. It's my job. I think having kids at weddings is a great idea. They bring life and vibrancy to a wedding - IF the wedding is set up for kids to have fun AND the bride and groom agree that children should attend. I would say at least 70% of the weddings I photograph have children under the age of 8ish in attendance.
However, I've seen enough wedding ceremonies and receptions turned into a nightmare by children's behavior I can totally understand why some couples would request that parents refrain from bringing their children.
This is not an opinion - it's a fact - weddings are private affairs and the bride and groom have every right to restrict attendance to adults only. I have actually witnessed guests being required to sit in the foyer of the church with the doors closed (or outside the church) while the ceremony proceeded, and then politely instructed - not asked - to refrain from bringing their children to the reception.
At one wedding that was restricted to children over the age of 12 only, a mother with a 5 year old boy came in through a side door and moved my bags from the chair the church had reserved for me (sign on chair) and sat directly on the aisle. Before I could turn around, the kid pulled my bag off the next chair and my $4K backup camera setup was knocked to the floor. The annoyed mother then said, "it's best to put that stuff somewhere safe". I asked her if she had her credit card present. I was 100% serious. If that camera had broken - thank goodness it was fine - I would've brought her to small claims court to foot the repair bill. I'm not a big meanie, but I'm not in business to take an equipment loss or get dropped by my insurance company due to a small claim. Parents MUST control their kids at functions like this.
I've also seen expensive flower arrangements pulled over, waiters trip over kids and spill food (try paying $100 per plate), people go nuts because children disappear and entire receptions grind to a halt for 10 minutes trying to locate them, kids *nearly* pull an entire cake off the cake table, kids opening gifts from the gift table, and two totally obnoxious eight year old boys defacing the black and white images in a custom (expensive) signature book the bride and groom paid me a lot of money to produce for them and the parents leave without apologizing or reprimanding the boys. I've seen parents completely ignore their screaming children who really wanted to go home during the reception, let their kids run around unattended at very posh locations, allow their very young children to play in bathrooms and near the shoreline of Florida lakes (can we say ALLIGATORS that eat small things as a hobby?) and let oh-so-cute little Suzy follow the bride so closely she tore half the trane off a $5K dress during the first dance while the mother egged her on so she could get a few pictures.
Listen, if someone says DON'T bring your kids, then don't. Even if you ask nicely and they say you can later. Just don't do it. Even if you traveled hundereds of miles to be there and your babysitter didn't show up. If you do bring them, other parents who went through all the trouble of finding child care will surely get mad because you didn't have to. They won't get mad at you. They'll get mad at the bride and groom.