It's one of those things that's like "write one HTML file with zero styling, then you can have multiple different CSS files style the same content completely differently! Separation of Concern!" Sounds perfect in theory but just doesn't always work.

Having one API for web and mobile sounds good but in practice often the different apps have different concerns.

And SEO and page speed were always reasons the server never died.

In fact, the trend is the opposite direction - the server sending the mobile apps their UIs. That way you can roll out new updates, features, and experiments without even deploying a new version.