Cricket Australia's decision not to reveal an investigation into Tim Paine by the sport's national integrity unit has been criticised by commentators following the former test captain's resignation on Friday.

Paine quit the post less than three weeks ahead of the start of the Ashes series against England after admitting he had been investigated over messages he sent to a former Cricket Tasmania female staffer in 2017, prior to taking over the captaincy.

"By making the decision not to bring the issue to the public eye...the leadership of the day showed a preference for brand management, as opposed to the real and lasting cultural change that was promised by CA after Newlands," Daniel Brettig wrote in the Sydney Morning Herald.

The wicketkeeper had been cleared of wrongdoing in the 2017 inquiry and was seen as a safe choice when he was appointed to replace Steve Smith in the aftermath of the ball-tampering scandal involving his predecessor in South Africa in 2018.

But Paine stood down after Melbourne's Herald Sun newspaper published alleged text message exchanges between him and an ex-Cricket Tasmania employee, claiming the co-worker had complained that he had sent an unsolicited picture of his genitals.

Cricket authorities have rallied around Paine, revealing that the woman complained to them only after she was charged with theft in the wake of resigning from her job.

Paine's "interaction" with the woman was "consensual, private, occurred on the one occasion only ... and was not repeated," Cricket Tasmania said.

"Paine's embarrassment is, obviously, acute; so will be that of his family, on Friday unseen, but, no doubt, privately suffering," wrote The Australian's senior cricket writer Gideon Haigh.

"Yet CA's board has effectively chosen to add to their mortification, because to do otherwise is to endanger its corporate reputation — the reputation Paine helped hugely to rebuild."

Meanwhile, former Australia international Greg Chappell has backed vice-captain Pat Cummins to be take over as Paine's replacement.

"The fortunate thing is that in Pat Cummins, they have an excellent candidate, ready to go," Chappell wrote in the Sydney Morning Herald.

"Like Paine before him, Cummins will be required to not merely lead the team but again rebuild faith in the role and Australian cricket."