I think the Kings are a good team and made intelligent changes in the prior off-season and in-season, IMO they were far more competitive and scary this season then they were last season and wouldn't take much more to break through.
I think stylistically the Kings lock down defense style just doesn't work against the Oilers, it's one of the few teams that can seemingly overpower and break nearly any defensive gameplan, the Oilers weakness is more fast and aggressive forechecking, rather than trap defense.
Then the secondary issue is the mental toll repeated losses to the Oil have had on the team, their confidence seems fragile when things aren't going their way (especially against the Oil).
Thirdly just some dumb decisions by Hiller these playoffs, really made it extra hard on the Kings.
I know in the East the Kings are talked about as some joke team cause they keep getting bounced in the first round, but in the West I feel like there is a lot more respect for what is a very capable team.
IMO the Kings are good enough that based on the respective 1st round performances this season I think they could of beaten: WPG (Hellebuyck sucked), STL, MIN, OTT, MTL, NJD (critical injuries), and WSH (the last one is controversial, but I generally bet against teams with unsustainably high PDOs).