f the code has a function foo(), and you have dilligently added one or more tests in your comprehensive test suite that exercise foo(), then instrumenting your test suite is never going to tell you that your code no longer calls foo().
Granted, but you could remove the tests that explicitly test foo(), and see where you stand. If nothing in your code library calls it that would at least tell you that your own code doesn't use the function.
And this is far from the only situation in which test suites give you a falsely heightened sense of well-being.
I'm not really clear on what you're saying here. So, because test suites give some programmers a falsely heightened sense of well-being, no one should implement test suites?
A test suite is not a silver bullet, it's simply a tool to help you solve problems with your code.