I think it's generally used to load the nine or ten different analytics, segmenting, crash reporting, user mouse movement tracking, A/B testing, etc frameworks that every site seems to have nowadays. Using Tag Manager means that when the marketing department decides they need to add another framework they can just click some buttons instead of having to ask a developer.

Since none of that stuff is necessary for the site to work, leaving it blocked basically never breaks the website.

Really? In my experience, blocking GTM almost always breaks some core functionality of the website I'm browsing.

Yes, completely serious. I've enabled it once or twice to see if a site was acting wonky because it was blocked, but it was never the culprit.