Late dining reservations are great. We often have reservations near closing time, usually at Epcot, and have never been rushed out.
It's nice to stroll through a nearly empty park, sometimes going the long way around World Showcase giving us the opportunity to take some wonderful night time photos. The music continues to play even though it's long after closing. The whole atmosphere is so much quieter and peaceful - very different from the daytime.
I haven't tried it at Yak and Yeti, but I'm sure the experience will be similar.