You're moving the goalposts now; those are integration not unit tests. But the type system certainly can validate/enforce that the column you select from the DB into an integer, really is an integer in the DB too. OCaml does this with Postgres. It can also make sure the end result of a calculation is of the correct dimensions, that you're not adding cms to inches, etc etc.

A lot can be said with types beyond simply checking things like "is this a String or an Int?".

Depending on the power of your type checker, you can say (with varying degrees of convenience) things like "this integer will always be positive", "this is always going to be a non-empty list", "these two functions can be composed", "I've exhausted all possible values for this variable; I know it because the compiler told me so", "it is safe to call this function, and I know it won't touch the database or do any kind of I/O", and many more.

Whenever you called a function and it wrote to a file when you didn't want that, that's also a type error!