Not all thoughts are consciously summoned, wanted, or pleasant. The term intrusive thoughts is a good way to describe those thoughts we find unpleasant. Yes, they are natural and normal, and often how we grapple with and process experiences, but that doesn't make them unobtrusive.
Additionally, many people have intrusive recollections of upsetting events from the past. Intrusive thoughts is a good descriptor that helps avoid over using terms like flashbacks or PTSD.
Clarifying such things as intrusive helps destigmatize these thoughts for people who have them and feel the weight of social expectations, like new parents as in the comic. Feeling guilty about having these thoughts isn't healthy, and properly describing them as unwanted helps people process them. I don't see what is particularly objectionable or hard to understand about the term and why being more specific in the description of one thoughts is off-putting to you.