Whether the average random on the street admits it or not, people crave some kind of structure and meaning in their lives. Religion gave the public that, and while the youtube atheists were right in the inherent illogic of a lot of it, most people are not content to disrupt a system if it's perfectly serviceable for them. Look at the famous atheists of the beginning of the century. How many were normal people with family? I can't think of any. They were invariably gay, a bachelor of some description, or the type to earn their own thread on this very forum. They were never going to assimilate to the societal mode anyway, so what difference does it make to them if it all gets torn down?
The problem, and this is something to Peterson's credit he at least admits, is that a society with no shared values or principles isn't a society anymore. And an atheistic society is more of a transitory state than a solid end-point. You see it now with the SJWs, the alt-right, and the niche identities young people cling to now to give themselves something to fight for.
This happened in every generation but without a bedrock of society, you've got millions teetering on this tightrope of simultaneously being apathetic about death-- since their spiritualism is non-existent, while also being petrified of not leaving a big fat mark on the world, since the implication is a dark unconscious oblivion at the end of all this.
The spinsters 100 years ago that talked shit about the family who didn't attend church? Their descendants are the ones rambling about pronouns and cancel culture. It's the same neurosis, only today, those energies are socially destructive rather than reinforcing anything.
Same with the incel and the race theory spergs. In days gone by they would have been shunted off into a monastary and got to perform at least some kind of social good, learning off every obscure saint and feast day to make everybody feel better, rather than being ridiculed outcasts with a victim complex.
As for everybody else? This isn't the first time in history wages have been stagnant, or the future looked precarious, or there was declining collective bargaining power. Difference now is the support structures that helped everybody cope somewhat have been eroded. As in, having a caring family, or knowing your neighbours well, or lending people cash when they need it without expecting immediate compensation, that's all been maligned as low status and provincial. I saw a show about saving money before Christmas there, and one of the ways the financial adviser suggested a single-mum save cash (note; not get out of debt, not fix the income deficit, they were past that bit, but raw, saving up money for a trip abroad later that year) was to charge her teenage son rent. That kid didn't have a job, and if he has potential he ought to be channelling his energies into studying to get into college, not be made to work weekends so his mum can get a holiday. But when you view all your relationships through neoliberalism, everything is transactional. And that mindset is exactly what destroys the type of bonds that money can't replace.
In short, 'Clean Your Room' is like the atheism wave. It works if everybody does it, but most people won't, so you gotta think of ways to uplift everybody if you genuinely want to improve the world you're living in. It's Reaganomics taken self-help form. So from that angle I can't say Jordan Peterson's teachings are all that helpful going forward.