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%.
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.
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.)
"[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.