Earlier quoted context omitted.
Maybe it's a hazy memory, but from 2007-2011 my main computer was a MacBook Pro. I swear in that era, when an app wanted attention it would bounce in the dock endlessly. That was annoying, but it let you finish doing what you were doing until you were ready to switch focus.
I think you’re right - macOS changed this behavior at some point.
For example for this case, the taskbar icon would blink three times and then remain highlighted. So it would grab your attention, but not hold it, and then you could still easily see at a glance which app it was
At some point, like many other things, it looks like this either was changed or broke/doesn't work consistently. But I thought it was a nice design