This is really interesting and fascinating indeed, but it seems also very complex. A broad nice T-cell immunity seems nice, but at the same time a broader immunity must be ensured not to overreat or borderling to autoimmunity. It seems evolution has taken well care of this to keep it balanced most of the time. Many papes report that severeity of disease seems linked to either a poor T-cell response, or a too strong (or incorrectly regulated) T-cell response.
Severe COVID-19 infection linked to overactive immune cells
"Sometimes, our immune system overreacts to invaders, for example during an allergic reaction, resulting in
T cells killing normal, healthy cells and causing tissue damage. However, there is a ‘brake mechanism’ that should kick in, causing T cells to reduce their activity and calming inflammation.
...
On closer inspection of the mechanism, the researchers found that the protein ‘Foxp3’, which usually induced the brake mechanism, is inhibited in lungs of severe COVID-19 patients.
They are unsure why Foxp3 is inhibited, but further study could reveal this, and potentially lead to a way to put the brakes back on the T cell response, reducing the severity of the disease."
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https://www.imperial.ac.uk/news/206173/severe-covid-19-infection-linked-overactive-immune/
I guess the more specific B-cell response seems is filling a gap here as well, in beeing "safer", with less risk of overdoing things? Marking a disarming a virus is one thing, but killing a "potentiall infected" cells is certainly more drastic unless the malign status is 100% certain.