Each and everyone disease you listed here can be cured. Example, Syphilis - https://www.cdc.gov/std/syphilis/lab/default.htm
May never happen [0], but one can wish. Although it doesn't have a cure, the treatability, prevalence, and general harmlessness of herpes make it less of an issue than the "curable" STDs. Most doctors don't even bother testing for it [1].
[0] https://www.healthline.com/health-news/why-we-still-dont-hav... [1] https://www.cdc.gov/std/herpes/screening.htm
general harmlessness of herpes
You said there's "no cure." That's different. Reducing frequencies of a disease for which there is literally no cure in exchange for higher frequencies of a disease for which there is emerging antibiotic resistance is still a good trade.
The article you cite regarding rising STD rates claims the cause is "a decline in funding for state and local agencies working on prevention" as well as "an extreme lack of awareness about STDs and sexual health" and "doctors are not screening and testing for these diseases and patients [not knowing] they need to ask to be tested" [1]. The only link to HIV stated is "people are not afraid of dying from HIV," not a link to prep.
https://www.nbcnews.com/news/amp/ncna642161
Lol there’s no cure for syphillis, gonorrhea, chlamydia, hep b, genital herpes, etc.
The recent year over year increase in STD rates in the US has been very well documented. https://www.nbcnews.com/news/amp/ncna904311