So an argument based on VAERS (from an article that uses the phrase "Wuhan coronavirus vaccine," no bias evident there...) --which we know, doesn't tell us much on its own -- from two doctors who don't deal with infections diseases or vaccines. Cool...
I'll give you the study that vaccines that don't prevent infection could extend the infections periods of some, potentially more dangerous, strains. But, even that study says that when this happens, it "can create conditions that promote the emergence of pathogen strains that cause more severe disease in unvaccinated hosts." This is not a reason to avoid universal vaccination, but rather to vaccinate as many people as possible as fast as possible, or to develop a vaccine that works differently. They also say "This does not mean that such technologies should be avoided, particularly when alternative options are limited."
EDIT: Also, it should be noted that the Covid vaccines are not particularly leaky, since they are 95%-ish effective at preventing infection. Yes, you can pass it if you get a breakthrough case, but getting infected is statistically not very common. The Covid vaccines work, primarily, by preventing infection. They also, as the linked study suggests "keep hosts alive but still allow transmission," but only in the small number of breakthrough cases.