On my current project, for the first time in my long career, I have 100% code coverage. How I achieved it? By ignoring best practices on what constitutes a unit test. My "unit" tests talk to the databases, read and write files etc. I'll take 100% coverage over unit test purity any day of the week.
For example, imagine you're testing a calculator app. Your integration tests make sure that it never crashes, the UI works, basic math is working, etc, but maybe the sin() function is only accurate to two decimal places.
Edit: I do not mean to imply that you, specifically, are missing things. Rather, it is possible to write tests that have 100% code coverage while missing many possible bugs, and I think those risks are increased without the presence of unit tests.
That's absolutely right. 100% coverage doesn't say much. In fact, by itself it's a pretty meaningless measure of code quality. But the top-down idea still holds. In practice bugs are more likely to happen at the seams between components, and therefore it's where one should test first, not last. It of course depends on the type of the project but I believe it's true for the majority of projects out there.
Learned this the hard way by working on a million-line codebase for a couple years on a team. 40 minute test suite runtimes before you know if you broke something become a serious flow-breaker.
It is of course up to you if you want to design for scalability in the code sense, however.