I'm glad you realise it's unreasonable OP and factor in the cost and likely reduced adult guest list if all children are invited. Your friend probably has agonised over this, though personally myself I would have told my close friends in advance of the invites that we were only inviting family children.
My friend had a 'no relation cf wedding' had she not she would have looked at around 60 extra guests (the kids) and since affordabiltilty and venue size only allowed a certain amount it meant bumping half those friends off the guest list. They could have chosen another venue or spent shit loads but why should they. They had a lovely day in the holiday inn which was within their budget. They did tell friends in advance what they were doing and confided that they were sad to leave off children they were very close to who weren't family but the pure drama and angry feelings that would have come if they'd allowed 'certain children' just wasn't worth the stress.
The cut off point will always be: affordibility, venue size, guest list and in some cases, childs behaviour. Some parents let their kids run rampant, my cousin is bad proof of that, hence why my sister did not invite her children. She and her husband allowed their children to run screaming up and down the aisle at one wedding, yank on the bride's dress as she walked down the aisle, throw their dinner around, make loud demands and throw tantrums when not met (they just stood their trying to bride them rather then remove them from the room or take them to their own).
As someone said wedding stress comes from two sources- the wedding party or the guests. I never get why people get really furious if they don't like their wedding invite-just don't go, I understand the upset but fury-no. Same as brides/groom who get narky when people can't make it to stags/hens/wedding-it's an invite, not jury duty.
People have their own lives, that goes for guests and the bride/groom- different situations, different perspectives, different priorities.
I do expect one thing OP, I expect their will be at least one none family child at the wedding-not because they've been invited but because some people really are so self absorbed and entitled that, instead of cancelling, they'll do what suits them. Probably annoying the majority of other guests who have cancelled or found care.