Whats the mule do in the MMO or ATC tie-off

What does the mule knot add to the system? If I want to tie off an ATC to escape the belay, why tie a mule and overhand above the ATC instead of just the overhand?

I assume its important to keep the load off the overhand so that the overhand doesn't get cinched down and become hard to remove. Is this it?

You've answered your own question. If you just tie an overhand in the brake strand, it can move up/contact the ATC under load, and becomes much harder to release. The Mule is easily releasable under tension, and if tied right up to the ATC, doesn't allow rope slippage.

Thanks MP