I doubt this analysis. The base of computing where C++ is used is exponentially larger than the base where COBOL was used. In particular the compilers we currently use are written in it.
If the new language has good interop with the old then this doesn’t have to be painful either. A while back, I was working on a large Objective-C code base which was slowly moving to Swift. We quickly got to a point where new code was written in Swift by default. In only a couple of years, we had a code base which used Objective-C pretty much only in the dark corners where code churns slowly.