I'm no expert, but I think the STDs to be most concerned with those are those which are least treatable. Wikipedia says the ones you cite are bacterial, so I presume, completely destroyed by antibiotics.

So, viruses like HIV and herpes? And maybe HPV?

(still, perhaps the treatable STDs have already done some lasting damage by the time they're detected, anti-bacterials may be harmful, and it's still gross, so use condoms)