We just need to change the start date and end date. It is kind of ridiculous that a winter sport might end way later than the summer sport. I would be in much favor of having the Stanley Cup final being played in March. If we could see season starting in late August, we could see this end in early March. It does not make sense to have season starting in October when kids are getting started with their school in late August-early September with finals exam being in May-June. We need the maximum audience at this time frame so if they could end in March, you'd be getting a maximum audience. The goal is to make money so they should aim to achieve that goal.
Just to play devil's advocate:
If you put the Stanley Cup Finals against the middle of the NBA Playoffs, TV ratings will drop 20-25% which doesn't help make money. Blackhawks/Flyers were two strong markets but even they saw a ratings drop when they had a Game 1 conflict against the NBA conference finals.
A few owners don't want early season home games because there's a noticeable drop in attendance with football/baseball conflicts in some markets. Anaheim for instance tends to have Sunday home games so now they have to compete against Rams/Chargers (plus the Lakers who typically have Sunday home games).