Deaths aren't tracking cases, and the tests are probably too sensitive [0], so for all we know it really did wane in the summer. We're in a weird place with this virus in that we don't do anywhere near this extensive testing for other viruses, so we don't actually know if this is normal or not.
[0] https://www.nytimes.com/2020/08/29/health/coronavirus-testin...
How do you know the virus wasn't waning? I have always anticipated that summer was us giving us a break before it got worse in the Fall and Winter. Perhaps it is seasonal, we won't know until Spring. It may be bad in Summer, but really bad during the other times.
We won't know if it's false until we've experienced both summer and winter in both the northern and southern hemispheres.
Yes, cases increased were high in the summer in the US, but that doesn't tell us anything about whether it will be the same, or lower, or higher in the winter.
The common cold and influenza are seasonal in the sense that most infections occur during some time in the colder months.
The researchers were trying to figure out how long-lived immunity to other coronaviruses is. Their question was not about the severity of cases, but whether a reinfection is possible. They found that in most cases, levels of antibodies against 4 common coronaviruses spiked about a year after the previous infection.
That could either just mean that the patients still had immunity and their immune system was able to quickly produce more antibodies when they came in contact with the virus again.
But it could also indicate a reinfection. In that case, symptoms would be observable.
As symptoms were not recorded, we are unable to tell which case occurred more often.