Imagine removing antibiotics, vaccines, screening tools, and any other medical treatment.
Anyone who was around for the AIDs epidemic will understand how quickly a large segment of the population can start dying off.
The early portion, it was literally a mystery disease that was killing off anyone that engaged in risky lifestyle.
Most other sexually-transmitted diseases that existed in most of the world were unpleasant, but not life threatening, even before antibiotics. And it's also worth noting that most primates (and many mammals of all kinds) are not monogamous, and yet they are not plagued by STIs to any significant extent.
Instead, monogamy was much more important for managing babies, especially given how much hare human babies need, and for how long, compared to virtually any other animal.
As far as primates not having STIs, you might want to read up on the animal origins of HIV a bit. The only reason we have HIV is because SIV can proliferate indefinitely in another species and crossed into humans.
However, with a slow disease like syphilis there's also the issue of how well it was identified in old times. Identifying the primary form as sexual is very different than identifying the tertiary form as a continuation of the primary. It was 1965 before we realized shingles is tertiary chicken pox and the 1980s before they realized that cervical cancer is mostly tertiary HPV. Other virus/cancer links have been identified (I recently read that IIRC 5% of cancer is known to be of viral origin) and personally I think the actual number is even higher as determining a link between an asymptomatic virus and later cancer would be very hard. (Again and again I see news reports of clusters of unusual cancer where no cause is found but the pattern looks contagious. It's very hard for cancer itself to be contagious but the same effect would be observed if the cancer was due to an asymptomatic virus. I also find the notion that random mutations could cause consistent behavior of the cancer strange--but quite sensible if it's viral damage.)
As for SIV, I am aware of it, but it is not a serious problem for most simians (though apparently Chimpanzees are being killed by SAIDS in serious numbers) - which is my point. STIs have not been so serious a threat to animals as HIV+AIDS has been to humans in the initial pandemic.
If we have solved the public health problems, does it make Monogamy an empty construct? Or there are other social/economical/biological factors that hold it in place?