My oldest daughter met her husband in law school. He was Presbyterian, but went to Anglican schools. Great guy. He converted after they got married. They dated for years before they got married.
My younger daughter is a PhD in Psychology. She met her Catholic orthodontist husband on eHarmony. There is also at least one Catholic dating site I know of, maybe more.
As far as why you date, it is to get to know the other person and see if you are a match. I think the sex thing and the religion thing are kind of a litmus tests, among many other things that you discover through the process.
But dating is not absolutely mandatory. I can tell you that my wife and I met through our parents, but we lived in different cities. We had a two year mostly letter and phone call relationship before we got married. I would say we went out on only about a half dozen dates and we were the same town and able to be face-to-face only about two or three weeks the whole time. We are still married coming up on 40 years. I don’t recommend doing it that way, but it can work.
Here is one thing about being devout I think you are missing: Remember, it is not all about you. It is about God, it is about the children you might have and the love of your life. You need to put what you want about 4th on the priority list. Get out and meet people. All kinds of people. Get interested in them and befriend them whether they are potential mates or not. Volunteer at church. I guarantee that at least half the families at any Catholic church know a Catholic single girl who is looking.