Some criticism to the article:
The "more unit testing" section reminds me of junior devs asking why they can't test private methods in Java. If I'm testing a unit, I want to test the contract it promises (in this case, a method that does some checks and then sends something). That the behavior is split between multiple methods is an implementation detail, and writing tests around that makes changes harder (now I can't refactor the methods without also having to update the tests, even if the contract doesn't change) and it doesn't even test the contract! (There's nothing that makes sure that the mail is actually sent - we could be testing methods that aren't used by anything but the test code)
For the "easier to test IO" section: just don't. Your tests now depend on some in-memory implementation that will behave differently than the real thing. That's just mocking with extra steps, you still don't know whether your application will work. If you want to do io, do the real io
"Separation of logic and IO": this is in general the right thing to do, but the way it's described is weird. First, it does the same as in the "more unit testing" section with the same problems. Then, the code is refactored until it's barely understandable and the article even admits it with the Greenspan quote. In the end, the production code is worse, just to ... Not test whether there's actually some code doing the IO.
I actually think there are some good ideas in there: separating the logic from the IO (and treating them as separate units) is important, not just for better testability, but also for easier refactoring and (if done with care) to be easier to reason about. In the end, you will need both unit and integration tests (and if your system is large enough, e2e tests). Whether you're using mocks for your unit tests or not, doesn't make much of a difference in the grand picture.
Just don't mock stuff in integration or e2e if you absolutely can't prevent it.