"Unit" and "automatic" tests are not synonymous. We have a non-trivial system, and mocking the necessary components for unit tests seems like a productivity loss to me. But we absolutely have automated tests; we don't test components in isolation, but as they will behave in production.

However, carefully crafted system tests can exercise the parts of the system you want to exercise. You know the little examples you write up yourself to convince yourself that a new piece of functionality actually works? Turn those into tests, and keep them around. I have been saved by those when a seemingly unrelated change caused an error in something I had not anticipated.