Well, the problem happens when some technology evangelist or manager who doesn't know a damned thing about the existing system claims it's easy to migrate it to modern tools. .....
Sorry, disagree. Disclaimer: I work on legacy systems, and they've provided me with $$$ for many a year. But for 'legacy' I prefer 'industrial-strength, production' that happens to run on a mainframe (or Enterprise Server - whatever).
But I digress... these old systems are massively tailored (I'm on one now...) and have been doing the job for decades. But saying that they're not easy to convert or replace is obvious (if you mean it's difficult) or wrong (if you mean it will never happen). Modern IT tools and techniques (pick your favourite ones and insert in these brackets) can solve complex business problems. Might take a while to work out why the original did that thing it does on March 14th if it's a Tuesday... but that's tailoring.
If it's a problem that can be solved by IT, then IT can solve it.
Now another question ... should the existing system be migrated or totally replaced? I've got four or five old clunkers here that make me weep, and I'm leaning towards replacing the functionality with nice, modern easy-to-understand stuff. Keep the business process, replace the code.
BTW, where do I apply for this GBP135,000 job?