ESPN2 - already catches NCAA football and NCAA basketball, occasionally MLB, most MLS. Right there, you're clogging up a huge part of the prime-time schedule. Maybe you get early-season coverage because CFB doesn't play all 7 days of the week [though it's getting closer every year] but that gets you about 6 weeks; after that, it's CBB and all the preseason and early season hype - and with the B1G going to a 20-game schedule and starting league play early and the ACC following suit, there's going to be a need to put those games somewhere for prime-time viewing.
The NBA playoffs may start after the NHL playoffs, so that buys .... what, a week? Besides, ESPN will be capitalizing on the playoff push for teams trying to lock down a spot, and positioning among the playoff teams where those battles are still going on. And, MLB will be cranking up so there will be considerable coverage thrown at it. And, all the hoopla around the NFL draft.
After that? ESPN will be showing NBA games at every chance, because it has an albatross of a contract that requires it. MLB will be cranking up. The post-draft hoopla. Remember, NBC was able to put playoff games on CNBC as needed; is ESPN going to clear off space on ESPN Classic or ESPN News to do that? Because it sure as hell isn't clearing space on the main network for it, it likely doesn't have room on ESPN2 early on, and I'm not sure the NHL is really better served being on ESPN2 or lower in pieces, wedged in between wall-to-wall programming centered around other sports, than being on a network where it at least gets some kind of exclusive coverage.