I've found help at the nuxt discord channel. Here is the link for future references: https://discord.com/channels/473401852243869706/1293875986907004968
TLDR: The coupling between the nuxt page and the router is already implicit, so an explicit coupling is no big deal.
The guide is about not linking components to the router. This does not necessarily include pages at nuxt.
You could just bind the route params from page level into the component and leave the component unaware of the route and page if reusability is a thing.