Herd immunity works only if there is a sufficient rate of vaccine take-up; the danger is for the unvaccinated child who comes into contact with the disease later on (because generally anodyne childhood illnesses can often be devastating in adolescence or adulthood) and particularly for those children whose immune system is depressed for one reason or another.
Parents thinking oh I shan’t have my child vaccinated because everyone else is so there’s no risk for my child, reduce the number of vaccinated children so herd immunity no longer operates.
There have been cases of measles this year in Gironde precisely because of the drop in herd immunity.
The risk of bad side-effects from vaccines is lower than the risk from actually catching the disease, yet some parents count on herd immunity where there is no medical reason for their child not to be vaccinated.
I can, however, entirely see the problem with simultaneous multi-vaccine administration, I think it should be spaced out - but that it isn’t being advised purely for administrative reasons.
You are quite right, the threat is unvaccinated children coming into contact with the disease and each other.