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For what it's worth I don't think you're wrong with your choice, or suspension is useless per se. It's just that IMO presenting some features or accessories -invariably found on expensive bikes - as essential is basically suggesting that if you cannot afford them you can't carry your child. And that I think should be challenged, because not everyone can spend that sort of money, but all parents should be encouraged to ride with their kids, if they can safely do so.
What I mean is that we’re not searching for an absolute existential truth, so one person’s decision might be different from another’s and that’s ok. The cost / benefit / risk trade-off is personal and we can put our own choices across without having to convince others that they’re wrong. This isn’t Facebook last time I checked :)
For myself I’d never put my child in a tag-along trailer for example as I don’t trust motor vehicles - almost all collisions I’ve been involved in have been me being rear ended by a car that wasn’t paying attention, and anyway I want to interact with my child whilst riding, so a front loading bike is my preference. Yet both tag-alongs and long tails have been suggested to OP.
Same for suspension or ABS, the benefits may or may not outweigh the costs. It’s useful to hear that other rider’s kids aren’t that bothered about rough surfaces and maybe suspension isn’t always necessary. But remember that OP is asking about riding with infants / toddlers and specifically off-road.