Fixing income inequality creates more opportunities to perform activities, which leads to more socialization leading to more potential romantic encounters. Hard to think about a spouse when you're making $8/hr but spending 33% of your life behind a counter.

I also wager a portion of the people who feel they "need but can't get sex" may also learn that what they desired wasn't what they actually cared that much about.

In this regard, I guess one can argue that prostitution is a crutch to a much larger problem that may never truly be solved.

Do you think lower income people have less sex?

In the grand scheme of the world definition of lower income, no. I haven't looked too deeply into it, but apparently 3rd world countries have as much or more sex, but have less access to birth control.

In the context of "first world lower income", I'd wager there's a loose correlation. i.e the incel movement is one mostly formed from a frustrated lower-middle/middle class (which in the world context, means many americans for the sake of discussion). Another comment in this post heard something similar as well: https://news.ycombinator.com/item?id=27041400

I'd be interested in any studies that disprove this notion. I'll admit most of this comment is conjecture.

That also depends on other factors. When being a prostitute means being a criminal, obviously it's not desirable.