Fortunately there are a number of different ways to justify the efficacy of particular technology prior to its implementation that do not require millions of people to prematurely contract cancer. If you have a hypothesis about a particular long-term consequence that could arise, by all means let's design a system to investigate it.
I get that it is problematic to even vaguely cast doubt on something that is a big public health win, but you are ignoring the context I commented in, where someone said:
but can we really say with confidence that the scientific research done on vaccination hasn't been influenced in the same way
Do we know for certain that HPV vaccine research has not been influenced by the companies selling the vaccines?
Rephrasing, I wasn't doubting the effectiveness of the HPV vaccines, I was pointing out that there are vaccines that we can be pretty much absolutely certain about.