Interesting point. Foreign key failures are usually the result of a program bug. Unique and exclusion[1] constraints depend on concurrent actions, and can't be caught ahead of time as easily. So I assume you are mostly talking about CHECK constraints.
Also, we're talking about a single statement, which probably means a single table.
It does sound like a good idea to validate all of the check constraints on a table at once, and report all of the failures.
[1] http://www.postgresql.org/docs/current/static/ddl-constraint...
I like check constraints. I would never consider removing them under any circumstances, I've dealt with far too many databases full of inconsistent data. I'd just rather not have to duplicate them (or triplicate, etc) in each of my apps that accesses the database.