If you are hosting a bunch of services in Docker already it's easier to just add another image than doing something custom that you have to update in another way then the rest.
It’s not about adding complexity, it’s fitting it alongside all the other services you might run.
If every service, complex or as simple as a static site can be updated, stopped or having a backup done in the same way it makes things easier. Even if this very service wouldn’t necessarily need the complexity.