"We keep on writing unit tests because we know how much value they give us". As long as you do this, then you won't have only integrated tests for some parts of the system, and so those parts will not become more poorly designed as quickly as they would if you only had integrated tests.
When we have only integrated tests for a part of the system, then those tests don't criticize the design as well as microtests do. If we don't have constraints forcing us to improve our design, then the probability is higher than we will not improve it as much. This means more tangled code, which becomes even harder to test with microtests, which encourages us to write only integrated tests for that part of the system. Repeat.