Are you sure about that? You can validate an awful lot in a PostgreSQL constraint, and I often don't bother validating in the app as a result. Validation in the app can also be extremely difficult to get right in a concurrent environment. There is a high likelihood that many such checks have race conditions that you aren't aware of, if you haven't gone over your application with a dedicated DBA.
You're right that a lot is possible, particularly if you're willing to write a trigger at which point you have a programming language at your disposal. But it's not a great environment for writing code with logic, in terms of things like tool support, debug support, library ecosystem.
Yes, but I already have one of those in the form of a static type system. I dislike database schema for the same reason I dislike XML schema: it tends to enforce only the most trivial constraints, and means you duplicate part of your validation (because you still want validation in code for the things you can't check in the schema). It's just another moving part that can be a potential source of failures.