It depends what you use it for. I plan to use it for blog posts where I show the track of where I walked. I actually like that the map won't update. It wouldn't make sense to show me walking across a map of the future, would it? It's a record of the past and the map should be frozen just like the writing.

Sure, but in GP's context of local businesses, they certainly will want to keep up-to-date with any changes to make sure customers can still find them.

Yes, absolutely. I think, in that case, a managed tileserver (using PMTiles or otherwise) is probably the best solution.

Protomaps generates daily world files I believe [1] but I haven't confirmed that they're used by the download tool yet. In theory you can download the data everyday to pick up updates.

[1] https://maps.protomaps.com/builds/

Edit: re-reading top comment it looks like they're using a daily file so you'd just have to create a cron job