I don't think this is a 'most people' situation, it's some applying their own situation to others when there is a wide range of normal and an even wider range of mixed cultural messages about sex and emotions.
Not everyone gets sexual interest at the same pace, just like not everyone gets romantic interest at the same pace. Not everyone gets sexual interest before romantic interest or the other way around.
Some people do ONS, casual dating sex, three date rule, FWBs, and some people never do.
Some people try casual sex, don't like it, and choose otherwise after that (this may be the ones going on about you needing a rethink, presuming you'll regret it because they did) and some people try only close relationship sex and later get into casual sex.
Some people really enjoy sex but have no sexual interest in others unless they're emotionally close to them. They do not have celebrity crushes or get the appeal of one night stands - I've had some fun conversations trying and failing to explain it. I know people who've only dated friends they've known for a year+ not because of the time, but because they had no romantic or sexual interest develop until they knew the person well.
I'm practically the opposite - I can get emotionally invested quickly and intensely. Sometimes sexual interest arrives with it just as strongly, sometimes it comes later, sometimes it never does. I can't recall a time sexual interest came first, but there were times as a young adult I chose to have sex with someone sexually interested in me for fun/because I grew up with a lot of messages around sex, largely that sex as fun should be prioritised, that to do otherwise was 'old fashioned'/dull, that that's what "most people" do when not hindered by cultural messages and judgements otherwise. It took me time to see that those were also cultural messages and judgements, that I was just as much impacted by those as I was the ones that connected sex with feelings, bonding, and relationships, and to figure out what really works for me.