2nd masters... and PhD - I am impressed... and a lifetime ago I imagine that was really something; don't know about now, but I am skeptical. {and both of us an alumnus! 🥂}
Somewhat like yourself, I took the GRE and scored adequately but upon reflection I decided to pursue my own interests - educate myself. Of course such a curriculum would have some limitations and is based on some biases, but, to me, the key is to continue exploring where a vacuum is found. The process of education should never stop, but self-education is often essential.
As to your 'not taking the exam', you do not seem the sort to do the work but drop the rewards. I imagine you have made the best of your choices. 🛠️
>>As to your ‘not taking the exam’
No idea why, but I’m terrified of tests. Took an extra two years on my first masters to do a thesis instead. And as for the BU exam, the frustration was that what I was working on meant I knew more about the topic than the profs. Didn’t help. Basically gutless. Done well enough without it. Ran the professional society in our field, started two magazines, a professional organization, and ran 4 conferences. Took an entire conference to New Orleans so that I could take the executive committee to dinner at Jonathan’s. Have had an absolutely joyful time getting in over my head and doing so many fun things. Even retirement has been a blast.