Herpes isn’t a retrovirus. Nor is HPV, per OP’s specific example.

HIV and HTLV are the only circulating retroviruses known to integrate into the human genome. The only example of a non-retrovirus integrating into host DNA that I’m aware of (not to say there aren’t others) is HPV, which can unintentionally become integrated into host DNA due to DNA damage and subsequent repairs that incorporate the viral DNA. This isn’t so much a cause of poor clearance though, at least for HPV, as the integrated DNA isn’t capable of producing viable new HPV virions.