Just because Twitter does that doesn't mean it is the case everywhere else.

It moves some of the rendering work from the backend (having to query the data and generate markup) to the browser (query the API and generate the content based on the responses).

At my current job, it's made a significant improvement. The server returns compact JSON data instead of HTML, so it's easier to generate the data and uses less bandwidth.

It also looks faster for the user, because they change search parameters and only part of the page changes, rather than reloading the entire page.

As for "easier to maintain", that may be subjective. Code to generate a simple HTML template from results is replaced by JavaScript code to hit the API and generate the DOM. Although HTML5 templates makes that much easier.