No, it's not bonkers.
The less serious any given illness is, on average, the less obvious the benefits of vaccination are, both individually and on a population basis.
Individually because there are always some risks, such as an allergic reaction, infection at the needle site, or a contaminated batch of vaccine. These are rare, but can be serious. The trade off when they happen though, is against what is normally a mild illness. So it's much more of a question whether the risk benefit analysis is really positive.
On a population level the cost comes in to it, at least for public funding. Vaccination of a whole population is expensive, that money could be used for many things. Is it best spent on vaccination against an illness that rarely has long term serious effects? Quite a lot of jurisdictions would say no on this, there are too many other important uses for those funds.
Then there are all the issues around unknowns - for example, there seems to be an ever increasing number of vaccinations recommended. Could there be effects of consequences of that - maybe. And we might not know for years, or ever - look how long it took them to discover why leukemia is more common in developed countries with good health care, or the effects of depo-provera. Many people and many doctors have a general rule that all interventions, or sets of interventions, may carry complex or long term risks we can't easily assess, and so a good rule of thumb is not to intervene for relatively mild illnesses.
I would also say that I think that while it's true that missing work for an ill child has economic consequences, that is actually a poor reason for giving (or not giving) a health intervention to a child.