I understand the usefulness of the feature, but find their examples weird. Are people really exposing their company's databases and web hosts on their tailnet?

Yes I host web services for my consumption, like miniflux rss aggregator, that don’t need to be on the public internet.

Similarly I’m going to host my small business’ staging database on a home server and expose that on my tail net.

How is that different from exposing on the company intranet in general? Or hosting them in a publicly accessible AWS endpoint?