I think we need to be careful with our takeaways here.
The 17 years mentioned in the preprint are in regard to SARS, 2003 - not the common cold.
The “common cold” which Lund-Johansen mentions are specifically mentioned to be Coronavirus common colds, i.e. caused by other Coronavirus strains which circulate widely in the human population. It is likely you and me had an infection already. However, immune reactions caused by common Coronavirus does not last a long time. Months, maybe even a few years. In some cases, an early infection in your life could possibly last longer.
It has been discussed several times already that common cold Corona virus infections might be involved in modulating our immune system response to Covid-19. However WDKS about this, yet. We are truly in the field of speculation here, and it might even be possible that common cold Coronavirus immune response could make Covid-19 worse by causing a strong immune response (see: cytokine storm). Seriously: WDKS.
Just BTW, there’s one piece here which makes my head ache, a bit:
Researchers say among others that the reason why so few children get seriously ill from the virus is that they are more often cold-ridden than adults, and that means they have developed some form of resistance to the virus, writes The Telegraph.
I can’t read that Telegraph piece (paywalled), but this quote is presented:
Now scientists have suggested that children may be resistant because their immune systems are already well primed by the common cold. The common cold is caused by four different types of coronavirus which circulate in the community and are largely harmless. But while adults pick up a cold around two to four times a year, school age children catch an average of 12 colds annually, studies have shown.
This is the wrong chain of arguments. Children pick up common colds more easily (amongst other reasons) because they are immuno-naive, meaning that adults do not get infected as often because they already had been (often mildly) infected with the common cold, (ETA: see above, if you get infected early in your life, you might possibly have some immunocompetence for maybe even your adult life. Might. Possibly.)
Additionally, as you said, it’s not just “four different strains of Coronavirus”:
That’s again an example of bad pop-sci journalism, Telegraph. And the NRK piece is only mildly better, and worse in the aspect of paraphrasing a bloody paywalled news article instead of the primary source.
Bottom line:
I urge everyone here to wait until further research is published (and I mean peer-review published, not preprinted, and even then wait until the community discussed the results properly). I have some trust decision-makers will also do this and don’t jump to conclusions based on news reports.
At least in some countries. (Not so much in others - see: Hydroxychloroquine)