Part of me likes this idea. But there is one glaring problem - it almost eliminates any impetus for advancing if you're around the 9-16 range. If you had a traditional two 1-8 brackets for east/west, there's a "reward" for coming in 6th instead of 8th - you face the 3rd seed, not the 1st.
There's a few other problems. I don't think the NHL has the national-flavor of audience like the NFL to handle a lot of East-West games. Also, it wreaks havoc with the scheduling for playoff rounds - we now have a system where, in round 1, two games can start at 7 to 8 EST, and two other games can start at 9 to 10 EST. If you intermingle the East-West conferences, you could have 6 games starting in the Western Conference, and only 2 in the Eastern.
Plus, coaches, GMs, and owners will hate it. It's another opportunity for them to make a mistake and get their fanbase mad. Make the right selection? "Oh, we coulda beat anyone that round." Make the wrong one? "Should have picked X instead of Z. Idiot GM."
Add to that the owners interfering in hockey decisions. Let's say that one year, the Rangers are having a great season, and the Panthers are dead in the water, creating a virtual bye to the next rond. Bruins get to pick between the two. Does JJ sit back and let Don make the smart hockey choice? Or does he pressure Don into picking New York, because a NYR/BOS matchup will make Garden ticket prices skyrocket, while a FLA snoozefest will, to a degree, annoy the STHs (and professionals) who resell?