You're cherry picking situations to play up the leverage argument.
How many times does the setup man come up to pitch to the heart of the order with men on base and a one-run lead? If he gets through that, then the closer gets the bottom of the order with a one-run lead but in a clean inning.
Who faced the highest leverage situation there? You can't just go ahead and use the highest-leverage situations to try and defend the "9th inning is different" argument. In fact, i bet i can dig up seasons where, with a steady relief ace-closer combo, the main setup guy (ace) saw more high-leverage situations than the closer.
The 9th inning is not some magical animal like the unicorn. While it's true that some guys have a mental block and just can't do ti, the rule is that a great setup man makes a good closer, and there's plenty of evidence to back this up. A good relief pitcher will be good in any role, with the occasional outlier.
You want proof? you've got Koji right there. People here were moaning about his lack of experience closing, and look how that's turned out.