The store works. You have the products, the orders, the operations dialled in. Then you want a landing page the theme cannot lay out, a product page the theme cannot structure, a checkout upsell the theme cannot reach. So you install another app. Then another. The store gets slower every time you add one.
You have outgrown the front end while the back end is still fine. That is the exact case headless was built for.
Where it costs you: mobile. Google found that as a page goes from one second to three seconds to load, the probability a mobile visitor bounces rises 32%, and most of that load time is the theme and its apps. Source: Google, mobile page speed benchmarks, 2017.