An enthusiastic supporter has even published an advertisement, showing a face identified as that of Sir John Key transmogrifying into that of Luxon - the Electoral Commission is investigating whether its cost should be counted as an electoral expense.
There has been much speculation as to whether Luxon would make a good National party leader.
Most people seeking to pursue a political career do not announce their intentions in advance, but take the precaution of first joining the party of their choice as an individual member, then of attending local branch meetings, then of being nominated to the list of potential candidates and then of presenting themselves to a constituency party in the hope of being selected as a parliamentary candidate at the next election.
To attempt to short-cut that process shows, in my opinion, a lack of judgment and self-awareness.
Nor can we give him good marks for his political knowledge.
The notion that someone who has run a large corporation is for that reason well fitted to enter politics or potentially even run the country is a fantasy perpetuated only by those who are still mired in neo-liberal delusion.
Running a company (with - usually - the single bottom line of turning a profit) is child's play compared with the myriad responsibilities and goals - not only economic but social, environmental and international as well - required of those who want to help run the country.
As the example offered by Donald Trump shows, it is almost impossible for someone accustomed to simply telling employees what to do to adjust to a context in which everyone is entitled to a view and where people have to be persuaded rather than browbeaten.
But the real reason to react with scepticism to Luxon's self-promotion is that the record shows that business leaders often fail to translate their business success into political achievement - and on that subject I have some personal experience.
As a British MP in the 1980s, I had the opportunity of viewing at close quarters the fortunes of another businessman turned politician.
Sir John Davies was a very nice man who exhibited none of Christopher Luxon's unfortunate hubris.
He had been a successful businessman and had even become Director of the Confederation of British Industry before succumbing to the temptation to try his luck at politics.
He got himself elected to the House of Commons and was appointed to join Edward Heath's Cabinet as Secretary of State for Trade and Industry.
The poor man found his appearances in the House to be a nightmare. He simply could not adjust to a scenario in which everything he said was subject to immediate challenge, scorn and ridicule.
My own direct experience of him came at a later stage in his political career when he chaired the Scrutiny Committee of which I happened to be a member.
The function of that committee was to keep tabs on how far European legislation impinged on British law.
On that subject, his and my views diverged somewhat (he was a Euro-fanatic) but we managed to rub along together quite nicely and I was pleased to see that he found the committee a more congenial environment than the House itself.
But his example (as well as countless similar others) should be a warning to Luxon and the National Party. Luxon-style hubris is so often followed by nemesis. Simon Bridges can sleep easily in this instance at least.
Bryan Gould is an ex-British MP and Waikato University vice-chancellor