Yes, I would. However:
A) In such cases I think testing against the real thing often has a greater chance of catching subtle bugs rather than the automated test scenario against the elaborate mock which is highly likely to share many of the same assumptions that caused the bug.
B) Code reviews ought to flag that a piece of code that is not under automated test is being modified and appropriate care should be taken (ideally this alert should be automated but I haven't yet reached that level).
I think it pays to approach these things on a case by case basis, and if a pattern of subtle bugs does appear that's a strong indication that you should change your behavior (I'm a stronger believer in bug retros than I am in any kind of testing dogma).
>How many customer minutes lost = 1 developer minute
Is that a relevant question to ask? If you introduce the presumption that an automated scenario test is more likely to catch a bug than a manual test then I guess it's relevant, but honestly for these types of scenario I think the opposite is true.
I didn't mention it before also but if you have manual testers on hand that changes the calculus too. I'd say it's normal for 3-4 manual tester minutes to be equivalent to about 1 developer minute.
As I mentioned above, I really don't think it pays to be a test fundamentalist.
>That said, I think tests are the most expensive and most brittle way to address this problem.
Or a type system fundamentalist.