Rails and Testing, why testing controllers is not enough?

I was wondering, as testing a controller in rails run the associated views (even if not shown) and integrate many models concerns (by saving, updating,...), testing controller should be almost enough for all applications near enough of CRUD classical architecture. Am I wrong? Furthermore, views can be tested in the browser, as eyes can be quicker to check than describing everything in a test (and they can achieve CSS control too.)

Thank you for your point of view!

PH