A few truths:
Every team sport in the Olympics uses professionals.
The two summer sports added for the 2016 programme were added based on the professional bodies agreeing to create a participation window and send their professionals (The PGA Tour and the European Tour agreed to create a window for golf, and the IRB and its member nations strongly lobbied for and agreed to release players for a sevens tournament). It's a reason why baseball got bounced off the programme (because MLB wouldn't release players).
The old Soviet Union teams...those were professionals in every sense of the word but hiding under this sham of being amateurs.
The IOC wants "the best" at its program, and no offence, that means the NHL. Getting the best draws attention which boosts rights fees; this canard about amateurism died a long time ago. Whether its boot money, per diem, the magic envelope, sham jobs, payola...whatever...have a damn funeral for it for all I care but let it go. The Olympics are about one thing...money. Think about 1992...the "Dream Team" in the summer games...don't think for a second the IOC didn't make a few bucks on that deal.
Football (or soccer)...has a model I keep saying would work- turn the Olympic tournament into an age group tournament. Football uses a U-23 tournament (with professionals), and each country gets 3 overage exemptions. You could modify it if needed.
The NHL players want to participate, and their clubs want some form of dispensation/insurance against injury and don't want to foot the bill. Seems like there needs to be some form of shared liability among the NHLPA, the league, and the federations. Of course the league doesn't even have a transfer agreement with the big European countries, so see how that's going.
You have Great Britain needing a small army of participation slips from FIFA, the IOC, and the individual nations of Scotland, Wales, Northern Ireland so they can enter a football team without fear of losing precious influence (and votes) within FIFA (talk about a s**tfight) in 2012 (because Great Britain competes as a unified team in the Olympic but individually in football they've never entered the Olympic tournament)...makes the "why doesn't (insert name of location) have their own Olympic hockey team" seem even more silly.