The NHL just will never get a big audience unless the teams are from the East Coast or Great Lakes regions, or are the LA Kings (See: The last 8 Finals, with Chicago, LA, Boston, Pittsburgh, and Detroit winning one or more Stanley Cups each). NBC got lucky with the Penguins this year, but San Jose is a nonentity regardless of how good they are. I wouldn't have been shocked if NBC moved the entire series to NBCSN if Tampa Bay had beaten Pittsburgh. Sun Belt just doesn't work in hockey.
Those "recognizable characters" are or were also among the best in their respective sports. Once they fall from the top, they don't draw the audience they used to, other than people who like to watch train wrecks. Tiger Woods and Kobe Bryant come to mind immediately. Peyton Manning came close, but was smart enough to quit while on top.
It also has a lot to do with the fact that the Warriors and Cavs are the two best teams in the NBA, with the two best players in the league and supporting casts like the great Celtics, Lakers, and Bulls teams had in their heydays.
People expect top quality play in the postseason. Most of the preceding rounds of the playoffs were a joke because the league just isn't anywhere as good as it was in the Golden Age of the NBA (1979-1998), and it may never be again. There are only four really good teams worth watching in the league right now -- Cleveland, Golden State, OKC, and the LA Clippers, and the Clippers went down early due to injuries. I might add the Spurs, but they're aging. Then look at the top-market teams that are completely in the tank (Knicks, Nets, Lakers, Sixers) or are just mediocre (Bulls, Pistons, Wizards, Mavs, Rockets). These have been among the greatest teams of all time, and were (still are for some reason other than market size?) attractive to the networks and advertisers, but they stink on ice now.