There’s some evidence that access to pornography decreases sexual assault and child abuse. The proposed mechanism is that horny people get to watch more porn, and this makes them less sexually frustrated, which makes rape seem less tempting. Analogously, violent movies seem to reduce violence in the short term. Slate Star Codex discusses both of these effects here. In particular, this linked paper considers all the objections that I’d thought of and seems pretty reasonable.
But rape is pretty dangerous and immoral. Most people do less extreme things when they’re feeling libidinous. For example, they might try to have one night stands, or might try to find a sexual partner. If access to pornography has a big enough affect on rape to be measurable, it seems very plausible that it would also cause a noticeable reduction in dating and casual sex.
I would love to find data to test this hypothesis. Rates of sexual assault are measured quite carefully and are publicly available. I’m not sure of a good proxy for rates of romantic relationships. Some shitty ideas include: flower sales, rates of bookings at nice restaurants, pregnancy rates, contraceptive sales. You’d have to be careful when during this analysis, because there are lots of confounding factors and I’m not sure how they play into each other.