Just because you have paid to reserve your seat, doesn't mean you also get to dictate who sits next to you, whether it is a child or not.
Maybe the airlines should bring in an extra charge for people who are scandalised at the idea of having a child next to them who might not be right next to their parents.
If I felt my children needed constant supervision, I might pay extra to sit next to them. But I don't feel that, and so no way would I pay extra.
I actually hate choosing a specific seat, I'd much rather be randomly allocated one. In fact, perversely, I probably would prefer to pay more to not be able to choose a specific seat.
You have only paid to reserve your seat, if my child is seated next to you it is not your affair or concern, or responsibility. I'm not paying an unnecessary fee because someone might not want to sit next to my child. I will ensure she is well-behaved, if she starts to vomit (unlikely) I will come and take her to my seat. But as her parent it is up to me to judge if she can sit apart from me, and I judge that she can.
What next - should overweight people have to pay extra to reserve specific seats because people might not want to sit next to them? People who smell? People who suffer from travel sickness? Perhaps people who want to recline their seat should pay extra because people might not want to sit behind them?