Psychological doesn't mean "you can't become a functional human without it". it means "without it, the mental state of a significant amount of humans will be altered". Under that definition, there is certainly an argument to be made about sex in some forms being a "psychological need". which build off the 3 universal psychological needs of autonomy, competence, and relatedness:
https://www.ljmu.ac.uk/microsites/promoting-healthy-weight-i...).
There are many much more well studied people who have spent much longer debating this, so I'm not interested in debating this here. I just want to note that valid arguments exist, and that I feel you are still conflating "basic" with "psychological".
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>Also, there are asexual people.
If you'd like another more controversial example: consider parental supervision. You can live a healthly life without ever leaving your parents' home nor ruleset. And in some other societies it is entirely expected to live in your parents' home even after marriage alongside one's parents (still following their personal values). However, some may argue that this hampers the psychological needs of autonomy and competence. That one will never have true control and choice and that you can never truly go out and challenge oneself while under a parent's wing.
Much like the basic "needs" of sex, this can be under contention and is ultimately up to society. A few anecdotes of those who made it or not doesn't rule it out as arguably being a psychological need not being met. Much like a few asexual people not necessarily ruling out sex as aruably being a psychological need at some leve.