I suppose offline access is nice. I think I'd rather pay for the ability to just download the whole site in some officially supported way. Priming a PWA baked into browser storage is a little roundabout. I want it to be grepable.
There used to be a tool I used that just downloaded all the files of a site locally that the browser requested. Would that be enough here or are you imagining something like it also points all the links to be local and goes and saves future pages as well?