What about the decision whether a function argument is an integer or a string? A floating-point value or an optional floating-point value? How could the compiler ever decide that?
The size of an integer is only a very, very small part of a modern static type system.
If a number is an int, float, large or what have you, the question I would ask is how many decimal points should be printed or if you divide 2 with 2, do you get 1 or 0.99999. A good language/compile should have sane defaults that works almost every time, while giving me options to override it if in testing it get an unexpected result where a human would disagree with the computer.
The source of tests should be the customer requirements, and types is just an set of automatic tests being applied on the code which has no direct connection to the customer requirements.
I have no idea what you're going on about. The customer doesn't care about the particulars of your unit or integration tests, instead they care about whether your software works properly. A modern, powerful static type system is one tool that helps a developer achieve that goal of properly working software, and the developer absolutely should care about whether that function argument is an integer or a string.
What I found problematic is that system and integration tests is generally relegated to be done outside of the programming process. It is instead the administrators job to write an extensive test system to verify that the program actually do the job that it was written for. You start to wish for a very different set of tool design when the programmer and administrator is the same person.