First impressions count, and the first impression people are going to get of the new government is that Peters is the second most important person in it.
The important thing is that Peters gets first go, the first year-and-a-half when the public's perception of the new government will start to be established.
Before Friday's announcement of the details of the coalition agreement and the cabinet line-up, Luxon described the deputy prime minister's role as "largely ceremonial".
He appeared to be trying to play down the importance of it and he went too far.
It's important and highly visible.
When the prime minister is out the country, as Luxon is likely to be on several occasions during the next 18 months, Peters will step in as acting prime minister.
He will be the one holding post-cabinet press conferences and, if Peters intends continuing as he has started, there will be some torrid encounters.
Prime ministers usually aren't in Parliament on Thursdays and the deputy takes over, standing in and answering questions from the leader of the opposition.
Labour leader Chris Hipkins is very likely going to try to goad Peters into an argument, which won't be difficult. Some sparky question times lay ahead.
Peters will make his mark and, as the Herald's Audrey Young put it, going first "will allow Peters to reinforce his position of seniority".
Being deputy also involves a lot of work in keeping up with the play in case the prime minister is incapacitated for any reason. An example of that was the six weeks Peters stood in for Jacinda Ardern when she was on maternity leave.
Paula Bennet, who has been a deputy prime minister, made that point when she was interviewed on Newshub's AM Show before the coalition announcement.
She also mentioned standing in at parliament's Question Time, which she said was a deputy's "time to shine".
As for the big picture - if Luxon had said at the start that he was going to negotiate a full three-party coalition government, the first of its kind in New Zealand's history, he would probably have suffered far less criticism about how long it was taking.
It was a huge task, getting three parties to agree on policy with the inevitable trade-offs involved.
The scope of the agreement is vast, and RNZ's 'Coalition Details at a glance: What you need to know' explains it all.
National's biggest loss was having to give up its proposed tax on foreigners buying expensive properties, which was intended to be a big part of the funding for its tax cuts.
NZ First refused to allow it, and now the lost revenue is going to have to be made up from some other source. When he was asked about it at the press conference, Luxon didn't say precisely how that would be done.
Seymour didn't get ACT's referendum on the principles of the Treaty of Waitangi, which National was never going to agree to, but he did gain a compromise.
A Treaty Principles Bill will be introduced to Parliament, go through its first reading and then on to a select committee. Support for it isn't guaranteed beyond that.
It's sure to be highly controversial, although less so than a referendum, and the select committee will likely hear hundreds of submissions. That should kick it a good way down the road.
A no-surprises line-up
Luxon has put together a no surprises, sensible looking cabinet.
There are 20 cabinet ministers, 14 National and three each for NZ First and ACT, with eight ministers outside cabinet.
Before the line-up was revealed, the only certain positions were Luxon as prime minister and Nicola Willis as finance minister.
Most of the other portfolios have been given to the MPs who handled them in opposition.
Chris Bishop with housing and infrastructure is third ranked in the cabinet, followed by Shane Reti with health and Simeon Brown with transport and energy.
Erica Stanford is next with education and immigration and not far down from her is a fully re-instated Judith Collins as attorney-general and defence minister.
As was widely expected, Peters is foreign minister and the portfolio of minister for regulation has been created for Seymour, which he wanted.
Luxon said at the press conference Seymour would be going through all government departments looking for regulations he could get rid of.
Seymour has for years been complaining about how red tape curbs development. He's likely to find a lot of it to cut.
NZ First's Shane Jones is in familiar territory as minister for regional development with a $1.2 billion capital funding for infrastructure.
Sorting out the differences
It's the first time cabinet ministers from three parties will sit round the table, and they will be bound by collective responsibility. Once cabinet has made a decision, all must support it and not publicly question it.
There's almost certainly going to be some hard talking at the table, because that's where any disagreements have to be managed.
It's clear that the three party leaders recognised the importance of handling difficult issues on which they might not agree.
Luxon said at the press conference a lot of time had been taken up with discussions on that.
The result was the establishment of a Coalition Committee which he said would be "a clearing house for any tensions or conflicts" between the parties.
"We know what we're doing is difficult," he said, and that was a good indication that they're not going into this believing it's going to be sweetness and light from now on.
There are sure to be problems and the government will do its best to keep them hidden.
That won't be easy. The leader of the opposition, the MP who will lead questioning in Parliament, is a very experienced parliamentarian.
Hipkins will be in his element, and with three parties in government at the same time the potential for leaks is considerable.
Caucus discipline for National, ACT and NZ First is going to be absolutely essential.
Hipkins didn't lose any time reacting to the coalition announcement and its policy terms.
"Christopher Luxon, Winston Peters and David Seymour have presented a grab bag of policies which - as Labour has always known they would - favour landlords over tenants, do nothing to prioritise climate change and fail to highlight any meaningful support for vulnerable New Zealanders," he said in a statement.
"Christopher Luxon has clearly made big concessions to appease his coalition partners… it's now not just a question of whether Winston Peters and David Seymour will run rings around Christopher Luxon, but how many."
Peter Wilson is a life member of Parliament's press gallery, 22 years as NZPA's political editor and seven as parliamentary bureau chief for NZ Newswire. This article was first published HERE