Your point is very interesting but moot because sadly Jim was completely finished with The Doors in 1971. I doubt that he would have even wanted to be part of a five man Doors providing lyrics whilst someone else stepped in for him.
By then he hated touring and was fed up with the audience who wanted LMF and the other hits. The rift between him and The Doors was far too great for something like that to happen.
Morrison LEFT the band in March 1971 so did not really care what they did.
He told them to carry on and suggested they do instrumentals.
Also you have to factor in the audience reaction to a Jimless Doors in 1971.
Of course after Jim died The Doors continued as a 3 piece (augmented to 5 for touring) but played practically all new material apart from a couple of Robby songs.
They played NO Jim Morrison songs in the two years they existed.
They did OK with an audience who accepted Jim was not gonna turn up but how they would have reacted to a replacement Jim when he was sitting at home writing lyrics is a completely different thing.
The band were seeking a lead singer before he left for Paris according to their manager.
They considered approaching Mike Stull from The Wackers.
Morrison never had any intention of stopping the band touring and playing anything they wanted with whoever they wanted.
It was THEY who made Morrison sign a document that disallowed HIM from calling HIS band The Doors without their say so.
After Full Circle the band tried to bring in Howard Werth from Audience and the British press actually announced him as the new singer with the band.
The idea that the band could have carried on playing with other singers is not sustainable really as even Ray saw that was a non starter and bailed out in 1973 just before Werth was to join.
As he said without Morrison there was no Doors.
back in 1973 I disagreed because I wanted to see Werth with the band as he was (and still is) one of my fave singers.
With the hindsight you mention I now see how wrong I was there and Ray was right.
30 years later the dogshit tribute act with astbury was a joke.
All that was about was Ray wanting to steal the band name, remove Densmore's veto power so he could sell Doors songs to advertisers and make a packet on the nostalgia circuit.
The only things it achieved was to destroy The Doors Internet community, make my favourite band a laughing stock and expose Manzarek as the lying hypocrite he was and is!