Yes I have instantly improved code by removing micro level solpisistic tests that were tightly coupled to the implementation. These tests made it much slower to improve the quality of the code and had zero benifits because they only tested that the code did what it did and not what it is supposed to do.
Good point, and I agree. Sunk cost fallacy and all that. I wouldn't consider those "objective", but I don't think it's worth arguing over the definition of that word when I think we otherwise agree.
I also would agree that sometimes time has been wasted creating too many tests. Perhaps that time could have been spent to greater effect.
I also think that even if, in retrospec, a test is very tightly coupled and specific to one implementation, that test still might have revealed bugs and may have helped the original author. If that test is now a burden, throw it away.
You appear to be trying some sort of reduction ad absurdum, but in many cases work on some change to the software starts with deleting all the related tests because they're going to be irrelevant and changing them isn't worth the extra work.
That that deletion is necessary means it apparently did make the code a bit worse.
Also all the time they were in while the code wasn't being changed, they made running the application's tests slower.
Objectively false, if not having tests is better than having tests then delete the tests. Instant improvement.
This fact leads to the conclusion that the value of having tests is greater than or equal to the value of not having tests, in all cases.