His argument makes sense. This of someone who is exclusively working with cobol and a specific version of a very specific mainframe. If he is staying there for 5-10 years, where would he go? Are these skills transferable? Would he become a data engineer maintaining Spark, no one would hire someone with a senior salary with no experience with a bit more modern stack.
In reverse, company is unlikely to let him go, sourcing a replacement would be a nightmare. This is a gold cage opportunity