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I've gone through various stages on my feelings about full coverage unit testing vs functional testing.

Having full unit coverage with full path coverage is a great ideal. The reality is that for most companies the overhead of having and maintaining these tests is impossible from a business POV. Getting buy-in to spend more than 50% of your time maintaining (writing, updating, verifying) tests is a very hard sell. For companies with under-staffed/over-worked development teams, it just doesn't happen.

At this point in my career I'm firmly in the camp that functional testing is really what matters in most cases. It is a compromise between the realities of business and the needs of engineering. I can test the end product of the development work as a whole and identify that everything works as expected and has no known strange side-effects. This also serves as a contract with your business users as to functionality of the product. If bugs are discovered you can add specific use-case tests to attempt to trigger the bug and prevent regression. All of this does not preclude limited unit testing as well for critical code paths. I find this to be a much more pragmatic approach.