Toby Young has quit the universities regulator, saying his appointment has “become a distraction”.
The journalist-turned-free school pioneer apologised “unreservedly” for a string of controversial comments he had made on social media in recent years.
But the public appointments watchdog said the “debacle” could have been avoided if applicants to official jobs were asked about their social media history.
Mr Young’s decision to quit as a board member of the Office for Students came after ministers were forced to defend his appointment in the Commons on Monday following a backlash from MPs, including prominent Tories.
His appointment was only announced on January 1 but created a storm of controversy, with a petition calling for him to be sacked gathering more than 220,000 signatures.
Writing in The Spectator, Mr Young said: “The caricature drawn of me in the last seven days, particularly on social media, has been unrecognisable to anyone who knows me.
“I am a passionate supporter of inclusion and helping the most disadvantaged, as I hope my track record of setting up and supporting new schools demonstrates.
“But some of the things I said before I got involved in education, when I was a journalistic provocateur, were either ill-judged or just plain wrong – and I unreservedly apologise.”
Commissioner for Public Appointments Peter Riddell said: “The Toby Young affair is essentially about politics, rather than the rules and procedures of the public appointments process.
“Yet there remains the question: are there flaws in the process which allowed the debacle to happen, especially in the area of ever-present social media?
“Without any doubt this row makes a strong case for more extensive due diligence inquiries by departments in any case of doubt about a candidate.”
He said that he was not usually involved in the appointment of board members and only heard about Mr Young’s role on January 1.
Mr Riddell said “the procedures have been followed in the formal sense of a fair and open competition” but he added that candidates should be asked whether there was anything in their past which could cause embarrassment.
In the Commons on Monday, then universities minister Jo Johnson said that neither he nor the department were aware of the offensive tweets before the appointment was made.
But Mr Riddell, writing in a blog post, said: “The problem with that view is that in Mr Young’s case, some of his offensive tweets were unearthed publicly almost as soon as his appointment was announced, and had been the subject of media coverage in the past.”
Highlighting the need for “due diligence”, he added: “The main lesson of this episode is that department and interview panels should not just focus on a candidate’s specific suitability for post.
“They should also press candidates on the potential embarrassment question, as they already do on conflicts of interest.”
Mr Johnson was moved from his post on Tuesday and given a new role in the Department for Transport as the Prime Minister carried out a reshuffle.
Mr Riddell said: “Ministerial responsibility means, of course, taking the criticism when an appointment proves to be controversial, as in this case. Due diligence matters and often saves later difficulties.”
After Mr Young’s resignation, Mr Johnson wrote on Twitter: “Toby Young’s track record setting up & supporting free schools speaks for itself.
“His decision to stand down from the OfS board and repeat unreserved apologies for inappropriate past remarks reflects his character better than the one-sided caricature from his armchair critics.”
But Education Select Committee chairman and Tory MP Robert Halfon said Mr Young had “done the honourable thing” in quitting.
Shadow education secretary Angela Rayner said: “The Toby Young saga has cast great doubt on the judgment of the PM, who failed to sack him in the first place.”
Conservative Party chairman Brandon Lewis defended Mrs May’s handling of the furore.
“I think she did show clear leadership in wanting a team of people who are passionate about education,” he told BBC Radio 4’s Today programme.