Tim Paine has recently said he has been proffered many opinions on when he should retire. He says he isn't going anytime soon.
On cricket forums, some former captains and media pundits, Steve Smith is constantly touted as next captain. Outside cricket in the milieu I associate in, Smith is universally condemned as a cheat. For many of the public outside sporting circles, his appointment would bring the game of Test cricket into disrepute.
The other mooted option in the media , Pat Cummins, may have the requisite leadership of player management skills, but has virtually no captaincy experience. In addition, Cummins has the onerous fast bowlers' workload.
The most established batters, including spin bowlers, who are probably best suited to the captaincy position, are Lyon, Head and Labu.
I'm firmly in the camp that Smith and Warner should never captain Australia again.