The NHL has stated their reason for keeping the Division structure is to foster and maintain regional rivalries. Nice theory, because otherwise, they don't make much sense. You do end up hating the teams you play against most, but it could be even better. A simple change to the playoff formula could make those Division games much more interesting.
What if the Division champion was decided based only on games within the Division? The Division champion gets an automatic berth, and the rest of the bracket is filled out like today, based on total standings points. It creates a season within the season -- 24 games that have double the importance of any other. These are the games that coaches will circle on the calendar. Players will lace the skates a little tighter.
The overall impact on the playoffs will probably be minimal. For a team otherwise out of the playoff picture, but who has had a decent year in the Division, it could give them something to play for. The downside is that it could bump a bubble team or two out of the playoffs.
It will be interesting to see what the Board of Governors decides to do with re-alignment. Next year they will have to deal with the Atlanta-Winnipeg relocation, and possibly a shift from Phoenix to someplace like Kansas City or Quebec. If they go to the 4 division structure proposed, this may not make sense.