I think that this scenario routinely happens at many companies. Only you don't hear public stories about it, because in the end what happens is the same for all

I think that this scenario routinely happens at many companies. Only you don't hear public stories about it, because in the end what happens is the same for all software: continuous transition/refactoring. I know I've been working on many projects like in these conditions, though not of that size. With more and more experience of that kind and by working on stinking code-bases, I've come to the conclusion that while in the past I could have thought that trashing the code and starting from scratch would help, now I would probably approach most problems by pushing new code in the form that I want and transition the rest as changes are required. I had projects that I did myself with great design care, but after 5-6 years due to shifting requirements also started to look like you could have done a better job by starting from scratch again. Reality is, in retrospect all code is suboptimal.