Cricket Australia handed one-year bans to Steve Smith and David Warner for their involvement in the ball-tampering scandal while Cameron Bancroft was given a nine-month suspension.
Johnson is not the first Australian cricketer to say that the bans should remain. Former skipper Ian Chappel had earlier mentioned that the bans should not be reduced.
Australian cricket is enduring one of its worst phases and a run of losses in recent times prompted calls to bring back their two star players before the contests against India.
Cameron Bancroft was the chief offender in the ball-tampering scandal in South Africa earlier this year in March.
The trio were suspended for their roles in the ball tampering scandal in the Cape Town Test in March where the former two leaders were handed a 12-month suspension and Bancroft given a nine-month ban.
New Australia coach Justin Langer and Test captain Tim Paine are charged with changing the culture within the Australian team.
Waugh has blamed the cricket authorities for letting the incident play out the way it eventually did and also protecting the players too much.
Warner played for the City Cyclones in the 50 overs match against the Northern Tide at the Marrara Cricket Ground.
The 25-year-old, who will be playing in Northern Territory's Strike League starting July 1, asserted that his current focus is to continue to perform well and earn his spot back in the Australian team.
Warner and Bancroft had opened the batting for the Australian side in the eight consecutive Tests before the pair was suspended from playing in the international cricket.
Bancroft is suspended from international and top-level domestic cricket for nine months and Warner for 12 months for their roles in the ball-tampering scandal.
Along with Smith, former vice-captain Warner and Bancroft have also been provided with the green signal by Cricket Australia to play in local tournaments.
Australian legend Mark Waugh has stepped down from the post of national selector after accepting a commentary job offer from the local broadcaster.
Bancroft, who is serving a nine-month ban for his role in the infamous Cape Town ball-tampering row, received 14 votes in his favour, allowing him to feature for his club side Willetton.
Steve Smith and David Warner have been cleared for the grade cricket while they serve the 12-month bans, imposed on them by the Cricket Australia over the recent ball-tampering scandal in South Africa.
Insisting that Smith was found guilty of negligence and that he was not a "cheat," Taylor said that he wanted to see the latter leading the national side yet again.
Australia's new head coach Justin Langer has left the door open for the return of Smith, Warner and Bancroft when their bans end.
Clarke said he would not like an Indian Test series victory over Australia to be undermined by talks over his country not being able to field a strong team due to the ban imposed on the trio.
Reflecting on the same, Australia's two-time World Cup winning skipper Ponting said that he was taken aback when the news broke out, but added that he is pleased to see the controversy is finally dying down.
Warner, Smith and Bancroft will now serve their suspension period as sanctioned by Cricket Australia after the controversial ball-tampering row.
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