I have tested my own writing a couple of times with these tools and, as you say, seeing those high burstiness and perplexity scores is affirming.

However, it's seriously worrying that these tools are getting it so wrong too. It makes me wonder about students whose work the passing of their degree depends on. What if their own writing is being flagged as AI and they fail because these detectors are so crap? It doesn't bear thinking about.