I find it useful in two ways.
First, if I am doing the same (or similar) workout a few weeks/months apart, the difference in power output may not tell me much, since it’s really just showing me whether my FTP was different. And if my FTP hasn’t changed, or I haven’t assessed recently, then the target power will be the same. But if I hit the same power output and my HR was lower, then it might indicate that the same amount of work took less out of me (i.e., I am more fit than before). If this same thing happens over multiple work intervals, and over multiple workouts, then I can be more confident that I’m seeing a real fitness change rather than effects of stress/sleep/illness.
Second, and by far the most useful thing of all: HR lets me see if I paused the workout, since this results in a “cliff” drop in HR. I haven’t found any other way to see whether and when a workout was paused. Being able to make it through a workout or set of work intervals with fewer/no breaks, or with shorter breaks (smaller cliff), can be an important indicator of improvement, even if the total work and output is identical.
That said, if I forget the HRM, I don’t get too wound up about it. It’s nice to have, but I could live without it.