That's not shockingly low at all. It's (a) a small sample size, and (b) in the dead-puck era. For that era, it's quite good.
Again, Kariya was one ONE POINT away from leading his team in scoring when they went to the Finals in 2003. The leading scorers, Oates and Sykora, had 13 points in 21 games. This was the height of the DPE, when a team scoring 2 goals per game like Anaheim could make the 7th game of the Finals.
As for not playing a lot of playoff games, that's what happens when you enter the League on a 2nd-year expansion team. The Mighty Ducks missed the playoffs in 6 of Kariya's first 8 seasons. But in their first-ever appearance (1997), they went as far as, say, Alex Ovechkin has so far in his entire career (with Kariya scoring 7 goals in 11 games). In only their third time to appear in the playoffs, they made the Finals and nearly won it all.
The Predators did kinda crap-out quickly, however, in the 2006 and 2007 playoffs, I'll give you that...