OP comes off as being extremely gullible with no street smarts. Probably right out of school. Govt IT tends to lag the private sector sometimes by decades. With all the Trump cutbacks who is going to fund new IT projects.
That's the benign interpretation. I'd say there's at least an equal chance that they, or at least Musk, knew full well the limitations of COBOL but liked the inadvertent narrative which aligns with his policy intentions.