Generally, the criticisms of running power that I hear fall into two camps. There's the "just run, baby" crowd. And there's the people who complain that "it's not really power the way a cycling power meter is." To the former people, I'd say that it's absolutely possible to get too wedded to the data, but there's also no reason not to collect it and make use of it when it makes sense. To the former people, I'd say that what matters isn't how the numbers are collected (and I won't even get into the fact that cycling power isn't as "direct" as they think it is), but rather whether the numbers are reliable. If you're using Stryd, they are. Stryd's running power correlates with oxygen consumption, which means it gives you a good snapshot of your metabolic output at a given moment.
I don't think running power will ever be as significant as in cycling because runners have the track. Pace on perfectly flat ground, on a measured course, is an excellent way of measuring effort in running. If cyclists all had ready access to indoor velodromes for training, then they could probably use pace for training as well.
On the other hand, if you are racing on a hilly course or if you want to do workouts on the roads rather than on a track, then running power can come in handy. Just think of it as an instant grade-adjusted pace measurement. People are actually very bad at measuring their effort on hills. I always thought I was a smart hill runner in that I'd let people get away from me early in races, and they'd eventually fall off the pace from pushing too hard on early climbs. After getting Stryd, it suggested that I should go even slower uphill, and the result was faster overall times and stronger finishes on hilly courses. On flat courses, on the other hand, I find it pretty pointless.
The other thing I really like it for is measuring peak power when I'm doing sprint work. If I'm doing 60 meter accelerations, hill sprints, flying 30s, or whatever, it's pretty hard to self-time yourself. And if you're going by feel, where you're only holding your top speed for a few seconds, then even an accurate stopwatch isn't going to tell you that much. But with a running power meter, you can compare all of your efforts and see what power level you were able to hold for a couple of seconds, which is not a bad way of measuring progress.