No surprise that WPEngine wouldn't support this - it has it's own system and i'm guessing thanks to the options you have with auto updates it would complicate things. With WPEngine your site is updated quick enough.

I am a little turned off by not able to turn on auto updates for THEMES and PLUGINS. I wouldn't be surprised if this is supported someday.

WordPress hosting - always expect restrictions, but I think WPEngine's restrictions still are reasonable.