I've never found this to be much of a problem in good code. API failures in front-end code tend to fall into a couple of buckets that can be abstracted away. If you want to preserve the page and keep retrying with exponential backoff, you can just implement that as a function that you then await until it succeeds. If you can't recover and just want to show the user a "shit's fucked, refresh the page" banner then you just need one handler near the top of the stack and let the errors bubble up. Most people are working in a declarative environment like React where you can just have a hook wrapping your API calls that exposes a potential error state to render accordingly.

You only really need to have try/catch blocks in 1 or 2 places unless you have a lot of novel async stuff going on that needs to recover from failures in specific ways. Most front-end code shouldn't have a try/catch around every API call.