> Tests can only tell developers they made a mistake. There is no gain at that moment.
The value is locating the problem code faster, and that generally can't be done efficiently in production. Outside a testing environment, you rely on logs alone to debug, or if you're more proactive you might grab session data but that means potentially sensitive user data is being cached and passed around to the support/triage team. At a security minded organization this should be impossible or at least difficult.
I agree it's not worth chasing Test Driven Development until you're actually testing during development.
This is a real problem, and it falls squarely on management. Testing needs time and resources, it needs priority and planning.
That's the reason I started speaking at conferences, started an online testing training course specifically for software managers, and am currently writing a book on the subject.