Erm... you forgot the elephant in the room. It's not so much about willingness but more about whom the NHL condescends to allow to participate in this tourney. You know, all the European hockey leagues are finished in time for this international tournament to take place in full strength, if possible.
I actually don't think the May time-slot is ideal for this tourney. It's nice they've been pushing it ever so slightly from April to May over the last couple of decades, to allow more and more NHL players to participate, but I believe the ideal time-slot would be February.
All the hockey leagues around the world should take a break of 2 weeks in Febuary every year, so that this tournament can take place at full strength, best-on-best. Cancel domestic all-star games for good, and cancel this tourney in Olympic years. That's it.
