The spike protein from the vaccine is injected into your muscle and does not circulate through your system.
https://www.youtube.com/c/Campbellteaching
https://www.youtube.com/watch?v=WuyAtvwP2H4
I personally feel its fairly compelling and I see no harm in performing this extra step to ensure its not being injected directly into a vein.
Not sure why the suggestion was turned down.
> This suggests that the use of antigenic epitopes of the spike as a SARS–CoV–2 vaccine might be safer and more efficacious than the full–length spike. Taken together, we identified one of the potentially important mechanisms of SARS–CoV–2 suppression of the host adaptive immune machinery. Furthermore, our findings also imply a potential side effect of the full–length spike–based vaccine.