Maybe it isn't worth it for you in the end after that conversation, but we should also not assume that the only way you get HIV is through "risky" behavior. That is irresponsible.
At least you would know it's an option and you can make the decision yourself, I know a lot of straight people that do not know prep exists because it just isn't talked about. Or maybe they have heard about it but they don't really understand what it is. That is a problem.
Through cost plus a month's supply is $14 (which means without insurance): https://www.costplusdrugs.com/medications/emtricitabine-teno...
Yes there is the additional costs of the tests on top of that, but people should already be doing regular STD testing if they are sexually active.
Regardless, nothing about that changes that you should still be having this conversation with your doctor if you are sexually active. I do not understand how this is an argument, a conversation about prep or doxy should be in the same conversation about condoms and your general sexual health.
The worst that is going to happen from that conversation is that you don't take it, but at the very least you are educated on its existence and that decision is made between you and your doctor based on your risk factors.
Edit:
In fact, the CDC backs up this opinion: https://www.cdc.gov/hivnexus/hcp/prep/index.html
> Inform all sexually active adult and adolescent patients about PrEP.
> Prescribe PrEP to anyone who asks for it, including sexually active people who do not report HIV risk factors.