I have been asking the same thing of friends and colleagues. I have heard that they are not necessary and also that they are crucial. Doing OSP on spin bikes, it has been nice to look at power in addition to HR.
It would appear that the biggest upside would be if you do similar workouts repeatedly, the power meter can tell you how you compare from one workout to another (HR training will tell you your heart beat more or less, but not whether you were hungover or tired). Combining HR and Power, you can see where your power is compared to HR (I.e. I don’t feel good and my heart is working overtime but my power is low so I’m probably having a bad day; or I just did that 2 hour workout in zone 2 but averaged an extra 25 watts for the ride, awesome). In theory, you would hope to see a steady increase in power over a period of time while your heartrate remains close to steady (I think).
On the other hand, it’s another set of data and metrics to follow (and a pricey one). so ask yourself if you are the data type. If you finish a workout and look at your distance, time, and pace then save, stretch, and move on perhaps you are not a data type. If you analyze the data from each workout to determine how to improve your next one (I don’t) then maybe you are.
I would like to have power data, but I am not sure I would analyze it sufficiently to justify the cost. It would just be another number for me.
