Another explanation is that the static structure diagrams are what give the C4 model its name: Context, Containers, Components, and Code. These diagrams existed for a number of years, before the addition of the other diagram types, which themselves supplement the static structure diagrams.

That said, I don't find myself using the dynamic diagram type all that often. For software systems of any size/scale, I'm not going to create dynamic diagrams for every use case/user story/feature/etc. Instead, I'll use dynamic diagrams sparingly to describe overall patterns in use, significant use cases only, or complicated sets of interactions between things.

To prevent the issues you mention about overlooking issues, especially when doing any up front design, I recommend "dry-running" the significant usage scenarios across the static structure diagrams and/or running a risk identification exercise (e.g. risk-storming). Or you could use a formal architecture evaluation technique.