More vaccines seems like one of the most straightforward future mitigations since viruses like Hepatitis/HPV/mono/HIV/herpes/etc cause almost a fifth of cancer cases: https://en.wikipedia.org/wiki/Oncovirus
That is a dubious claim. While links between HPV and cervical cancer are quite strong and well-defined, the associations with the other viruses you cite are only correlative. Also, Hep C, HIV and herpes have no vaccine, so unclear what your statement is referring to anyway? What has contributed to a drop in cancer mortality would be advances in treatment (like targeted therapies and immunoncology), better image/blood…
And poster's own link doesn't claim some of the viruses are actually an oncovirus.
That said, I don't think that pushing vaccines (either in research or into arms) for the listed diseases would be bad.