MITM attacks require far more sophistication and many more moving parts than just stealing data from a web server's memory. Just because you have the SSL cert's key doesn't mean you have the ability to use it to MITM a site.

I'm not saying what you propose is impossible; I'm just saying it's quite unlikely. Security is all about layers. You don't throw away a layer that could be effective at increasing security in the majority of cases just because there are some cases where it wouldn't work.