Every user group focus test I've ever done on an app with a janky UI has brought it up as a significant "The app is so slow!" issue. On the things I build users hate UI delays.

In areas where the latency has been solved, don't make the options worse for the user. There are bare minimums, but they are usually hard to mess up. Such that, if you are bringing something new to the table, focus on that first.

State management solutions like redux; nobody i know or have seen does it exactly the same, its really tricky to use and takes a long time to get the hang of.

That said, document.write is kind of special since it requires JavaScript to run while the HTML document is still open (so before it fires the loaded event). There is a reason this API is barely used today and mostly superset by appendChild.

Management is complaining that our website is less responsive than our competition's ...

There's a lot that can be inferred by e.g. looking at the event type or understanding semantics. I expect this to be better when the features near completion.