You're correct on all points in my experience. My previous contracting gig involved writing Windows Server based code for a UK mortgage lender that interfaced between the internet based Hometrack valuation service, and a Fujitsu ICL clone mainframe running the core Cobol system for the lender. The key point about that system is that it is the core ledger for all the mortgage accounts, which add up to many billions. It's the golden record of all the mortgage accounts and payments. Replacing it with a new buggy system based on the latest tech could kill the business.
