The man has to also bear the consequences in most nations, since he has to pay a lot of money. They like sex, but not at that price.
(Although having sex isn't something that you need to survive (like eating), or something that will happen embarrassingly for physics reasons if you don't choose a voluntary place to do it (like peeing), it is controlled by similar mechanisms thanks to evolution being evolution.)
It's a very common option. About 30% report non-use of condoms in their previous one-night-stand.
Most STDs are minor and/or easily treatable diseases. The worry about them has a huge moralistic component.
It works somewhat, but to a much lesser extent than, say, penalties for driving without carrying a warning triangle, which is a rational-brain activity. At some point the penalties are creating a cost that is bigger than the cost of dealing with the thing they are trying to prevent, while still not working all that well.
Anyway, that's extremely off topic. I think the point is that there's no shortage of babies wanting to get made, and if you want the population to make more babies, you should reduce the things that are preventing them from doing so, not add positive incentives (unless they cancel out negative ones).
I don't believe not using a condom with a Tinder date is an option, at least in the West. No matter how attractive and insisting the male is, a woman knows she is the one to bear the consequences. Even if they're on a pill, STDs are still a thing, so why take the risk.