Are these screenshots really that useful?

We think they are that useful.

There are tons of tools to help developers get alerted when something goes wrong.

To name a few:

Server error logs, response time graphs, server graphs, browser console logs, compiler warnings, slow query logs, worker queue size, CPU load, etc etc etc.

What is one of the first questions a support agent usually asks?

Yep - What do you see on your screen

So comparing changes is pretty helpful.