I don't like to think about type checking as unit tests because they approach the problem from a fundamentally different direction, and I worry conflating them could lead to writing the sort of bad unit tests people are talking about here.
Type checking, or static analysis in general, checks for the presence of a particular class of errors.
Unit tests check for correct behaviour, and in doing so imply a lack of any errors, types or otherwise.
While it can be good to use unit tests to check for regressions in a specific error, the core of your tests should be specifying the behaviour of your system, not trying to catch out any specific class of errors.
If your tests are busy looking for specific errors, there will always be some that you miss (type checking, even in Haskell, misses a lot of classes of error). If your tests check for correct behaviour, there can be no errors.
Of course, writing tests with perfect coverage and specifying all the behaviour is impossible, even more so when you've got actual features to get out the door. So any static analysis you're comfortable with can be great for making up some of the slack, but let's not pretend that in most cases we shouldn't now need to be writing those tests to check it does what it's meant to.
The place where this approach sometimes falls short is on the public API boundary, as I mentioned in my other post. Types can be useful there, so maybe my original assertion was a little too strong, but still types should very rarely mean less tests.
(Apologies if the post is a bit all over the place, redrafting on a phone is hard)