There's no doubt finishing off games is important, but it is more of a defensive/situational skill. I mean, in normal play you don't get points for clearing the puck out of the zone or other defensive plays like that.
If the League started from scratch today and didn't have all the history it has, I would have empty net points as a separate thing. Not because it's a slight on anyone who has a lot of them, but it would give more context to the general stat line and even create recognition for players being good in those situations. Most people don't dive into stats that closely and look at where the points came from.
For example, guys like Backlund and Cirelli are going to probably finish the season somewhere in the 40's, but their actual points are in the 30's with half a dozen (and counting) empty net points. Having the separate points would immediately tell you this is a defensive center who you want out there at the end of games.
Then you have Max Domi also in the 40's who you don't want out there.
But I digress. It's actually kind of weird no one in this league have put up more than 13 empty net points before.