Which part is untrue? That there isn't enough personnel or that it's a severely limiting career choice? Because what you're saying confirms the first one, and for the second one, not a lot of people dream of working on legacy stuff in a big organisation, and those are your only choices if you're a mainframe programmer. Say in the US, for mainframe work, there are what, 30 banks? 5 airlines? 20 insurance companies? Not a lot of choice, and it's doubtful they'll offer "perks" such as remote work.
Lots of government too. I worked at a government agency that ran it’s business off of mainframe. I worked there as a web developer and we had to consume data from the mainframe in our web apps. Very tedious process.
Yeah, the hiring process is often 6+ months long for half the pay of private sector jobs, and 1/5 the pay of the consulting companies they bring in to do the bulk of the work anyway.