I hear lots of interpretations of it. I could be misremembering. I'll take another look at it. Appreciate the specific points to look into. :)
"Second: I would suspect that there are far more new projects started today in C than there are in COBOL. C is in use (at least sometimes) as a voluntary choice, and COBOL is not."
If we're using that constraint, then Java and PHP are the example with Java for about any kind of app. A lot of people even like Java. They think it's great and hate C. So on and so forth. Yet, the popularity still tells me nothing as I got to watch Java get forced by Sun and others into its position step-by-step with insane amounts of work to get it to match performance and productivity of better-designed languages... partly successful there. It was actually experience of Java IIRC (later C#) that was the reason many people didn't think an OS could be done in a GC'd language. They mentally associated GC'd language with stuff like that. That a small team pulled it off in Oberon with a handful of people at a time porting or extending it is always news to Java developers I meet here.
Lack of context, bad design, meant to replace prior languages for most applications, platform orientation, and massive ecosystem + uptake + tooling make it a better comparison. So, I'll use it and COBOL next time.
Maybe anything that winds up trying to play in that "language for big corporate enterprise software" winds up like that?
What they have in common, as with C, is they were pulled or pushed in for ecosystem benefits + marketing then spread and sustained on that bases mostly. So much stuff written in them with so many talent or tools that they're self-perpetuating. I'm claiming most C adoption & entrenchment is the same phenomenon outside embedded or ultra-high-performance applications where use is quite practical. You constrained the COBOL example but I recalled popularity effect applied to Java, too.
Second: I would suspect that there are far more new projects started today in C than there are in COBOL. C is in use (at least sometimes) as a voluntary choice, and COBOL is not.