It's not unheard of. Some platforms offer New Relic RUM integration which breaks shit (like XML sitemaps).

I am guessing the hosting provider gets access to the information the client also gets, but that's just a guess without any evidence. It would just make sense in the absence of regulation.

This is something absolutely unthinkable in our company. However, we have heard of other providers using similar tactics in the past, so always do your research before trusting a provider with your website.

I work for a competitor and we definitely do not do this, so I don't think it's ubiquitous at any rate.

There used to be a lot of web hosting companies that offered free hosting and injected their ad frame.

It's very common with features like A/B testing, analytics, advertising and CDN.

This should be inserted by the customer instead of filtering traffic, but not necessarily. It's very user friendly to only have a button to turn something on or off.