Those wondering why people can be so naive as to expect the league and broadcasters to do this are outright ignoring that in FIFA, NFL, MLB, NBA, MLS and other leagues, this is common practice. The issue is that you DONT actually know when the game will start, given that every building has a different practice, and each night might have the pre-game ceremonies go 10, 15, or 25 minutes. So you sit there waiting. You want to attract new fans? What do you think millennial fans today don't want to be doing for 15 minutes after the supposed game starts?
Publish a puck drop time, and work back from there to begin your pre-game festivities. Simple to do. The OP is right. It is doubly important in the playoffs, as more teams start to copy Vegas from last year and the pre-game ceremonies grow more elaborate.