This is what happens when websites prevent an open Console/DevTools side panel. They basically have a main loop running, inserting a debugger; statement in various places where they're annoying, and they do that at 30FPS / 32ms so that the DevTools become useless because there's no way to "ignore" debugger statements.
This button was added to specifically combat that, and even then it means you can't use breakpoints at all. IMO the missing link is a way to specifically ignore a single debugger call.
The debugger lets you edit the code in the VM, so if there's a debugger call you don't want you can simply delete it and continue and it'll not show up again until you refresh
