We're damned if you do damned if you don't at this point. Even if Dean does go full rebuild, you're trading away Carter, Kopitar, Quick, etc. for a bunch of prospects/picks that may one day become Carter, Kopitar, Quick, etc.
That route will get us back into contention just as quickly as a coaching change will, i.e., not at all. Yes, our Cups originally traveled the road of #4, #2, and #5 overall picks, but tanking that hard is no guarantee. For every Doughty, there's an Aki Berg.
In my opinion, your core is set in Kopitar, Carter, Doughty, and Quick. They're as important to the LA Kings brand (and let's not forget that this league is a business, first and foremost) as they are on the ice. You're either going to find another run with those players, ala Pittsburgh or San Jose, or you're not. Don't have a Pavelski or Courture? Then draft and develop one. These players weren't top five picks.
Bad contracts and wasted assets are the bane of this team. Do whatever you can to rid yourself of contracts like Gaborik's, and go back to developing your own youth. Think out of the box like Chicago did with Panarin. That single signing is a huge reason why they're still competitive.
Dean just has to be better. As do Kopitar, Doughty, etc.