He's still dead. It ain't the Doors.

Oh, God, what a horrible mistake! But what else can you expect from guys who thought they could do without Jim Morrison and recorded two horrendous albums after the Lizard King's demise?
All of this could have been avoided if more people were familiar with Halsted's Iron Law of Personnel Changes, named after the late poet and rock critic David Halsted. This law applies to all rock groups whose members collaborate in the creation of a distinctive group sound. So-called bands like Nine Inch Nails and Dashbored Confessional, which are made up of just one guy who calls the shots, are not included.
Bands of two or three members cannot lose a member for any reason and carry on as they were. No Tenacious D without Jack and Kyle, no Police without Sting, Andy, and Stu. How can you lose 33 to 50 percent of your musical input and call yourself the same group? Replacing the lost member will not restore the status quo ante, because the new guy will have a bunch of new ideas and start nudging the band to do things differently. Result: a different band.
Bands of four or five can lose or replace one member, if he's the least important one. This is where the Doors screwed up. They could have lost Densmore or maybe Krieger, but not Manzarek and certainly not Morrison. On the other hand, the Sex Pistols did OK when they replaced Glen Matlock with Sid Vicious. Note: this only works once. Losing one musician to drugs or drink is tragic, losing two is just careless.
Bands of six or more can lose no more than two members of lesser importance. Therefore, Lynyrd Skynyrd ended when their plane crashed into the mountain, and that's that.
Let's look at a few more examples:
Led Zeppelin-- did the right thing by calling it quits when John Bonham died.
The Who-- dwindled into tiresome irrelevance after they replaced Keith Moon with Kenney Jones.
Nirvana-- for Krist and Dave to have attempted to continue after Kurt's death would have required even more stupidity than the Doors.
Joy Division-- instead of hiring a new male lead singer, they brought in a female keyboard player and came up with a new name that had Nazi connotations, like their old name. Thus they laid the past to rest and looked to the future, embracing both change and continuity. Probably the best re-invention of a band ever.
The Rolling Stones-- followed the Iron Law without appearing to. Brian Jones was a founding member of the band and got much love from critics, but by 1969 he was definitely the weakest link (look at him in "One Plus One," curling up in a corner and pulling his guitar over himself like a blanket). Replacing him with Mick Taylor left the Stones still the Stones. Replacing Taylor with Ron Wood in 1975 meant that Wood was simply taking over the Brian slot, leaving the band still 80 percent original members. And by the time Bill Wyman quit in '92, Wood had been a member for 18 years, long enough that he no longer seemed to be a replacement for anybody. And by then Wyman was the least important guy in the band.
I have gone on, haven't I? Enough for one night. Bye-bye.