Based on what are you making this determination? I have known people with fybromyalgia and chronic fatigue and it's outright cruel that a lot of people (including doctors) are telling them that it's only in their head.
Psychosomatic doesn't mean "only in their head". It's the opposite really, it accepting that the symptoms are real, but are being triggered or aggravated by something mental (stress, for example).
Based on our knowledge of how vaccines work there is no reason to think they would actually help after the active viral infection has cleared. But psychosomatic symptoms are extremely common.
Why? If someone is harboring a low grade infection because their immune system didn't rev up enough to clear the virus, getting a jab with something engineered to provoke your immune system could very well fix the issue.
Also, "placebo effect" is real. "Reversion to the mean" is also real.
There is no clinical evidence that those patients are harboring a low grade infection. If the virus was active and replicating then it would be detectible even at very low levels.
The way to prove a psychosomatic component would be to tell a group they had COVID, then give them a harmless drug that induces some mild but harmless symptoms.
Take the group off the drug and survey them in 30-90 days for long-COVID symptoms.
You could also play around with control groups, for example perhaps one control group is asked not to watch or read any news programming related to COVID. I think the results would be revealing.
Maybe, but you can't actually say that. "Psychosomatic" reduces to "Big Pharma is telling you your very real disease is in your head" from an optics standpoint.
Public interest in the putatively psychosomatic Morgellons disease spiked after Joni Mitchell said she had it. There was an outpouring of support for Mitchell, and criticism of Big Pharma, the government, and the media for not treating Morgellons with more gravity.
My dad "had" Morgellons. The disease itself isn't real, but the symptoms were very much a part of other issues he had. The problem with labeling things as psychosomatic is that it can cover up very real suffering brought about by other, related issues.