I’d wager it would cost a whole lot less to train devs up on the existing system than to rewrite. Without understanding the existing code, you’re going to have a tough time replacing it.

This seems like a hiring failure to me, not a tech failure. I've been hired on several occasions to work with a language I had zero prior exposure to, and while there is of course some ramp-up time I managed just fine and eventually became skilled and knowledgable in those languages.

I don't see why COBOL, mainframes, or whatnot would be any different. Perhaps the ramp-up time would be a bit higher, but most skilled programmers will manage. I actually wouldn't really mind working with any of that – I just never had the opportunity.

I work for a large consultancy - we have large teams dedicated to COBOL, and I believe others (e.g. CapGemini, TCS) do too.

I wouldn't claim they are any good, just mentioning that grads are being trained in COBOL.