This is a bit silly: either it's trivially true but irrelevant, if the claim is that there exist people who can live happy lives without (sexual) relationships; or it's flatly false, if the claim is that everyone can be equally happy without relationships as they would be with them.
Relationships bring significant happiness. People who are in relationships self-report more happiness. They're richer. They live longer lives. You might say that I'm mistaking cause and effect: maybe happier/richer/healthier people are more likely to enter into relationships? This is probably part of the effect, but not the majority of it. If someone randomly ends up a widower from their partner experiencing a sudden, tragic accident, their happiness doesn't remain level. In fact, it substantially decreases: widowers have some of the highest suicide rates of any demographic group.
Relationships aren't some crazy random idea that just happened to develop in 2020 USA. They exist universally, across all cultures and times. All of them consider a relationship as a good, important goal (even as the typical attributes of relationships do vary). It's hard to name any facet of culture as universal as that.