"[Epstein–Barr virus] has also been implicated in several other diseases, including Burkitt's lymphoma, hemophagocytic lymphohistiocytosis, Hodgkin's lymphoma, stomach cancer, nasopharyngeal carcinoma, multiple sclerosis, and lymphomatoid granulomatosis.".
https://en.wikipedia.org/wiki/Epstein%E2%80%93Barr_virus#Rol...
Some of the articles cited in that section have sentences like "1 out 2 (50%) adult analyzed cases was positive, with 50% of stained tumor cells (this patient was a 22 years old female, coming from Napoli);" that don't follow the necessary standard of evidence. I continued to skim the linked articles and they are all clearly correlative.
https://news.ycombinator.com/item?id=34367905
"...several herpes viruses, which two-thirds of us carry, induce tumors in animal species."
https://pubmed.ncbi.nlm.nih.gov/4353788/
"A herpes virus causes Burkett's lymphoma in humans; another causes nasopharyngeal cancer in humans."
The link between hepatitis and liver cancer is rock solid, to the point chronic hepatitis is the leading risk of liver cancer.
HPV is merely correlative, as well. That's basically how all endogenous cancers work. With Epstein-Barr Virus the association is quite strong, though the incidence of EBV-induced cancers doesn't seem to be quite as large as HPV--~1% vs 2-3%.
OP is talking about more vaccines as possible future mitigations - more vaccines as in new vaccines, not more vaccinations using existing ones (though that wouldn't hurt either.)
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.