I don't think this would be a good feature.
It's not the worst idea but it's just not worth the effort for SE to implement.
the result does not match the output you desire, it let's you review
the code with more understanding of the output
You can do this with the button below the code.
It would be a bad habit to run code before viewing it for security reasons. Today a safe sand boxed environment could have an exploit tomorrow or "harmlessly" crash your browser.
However, if you this is a feature you'd like to have personally, you may consider developing a browser add-on for it. If you do, consider keeping it open source in case others have an interest. Sounds like it could be a fun starter project in the world of browser add-ons.