Are people who regularly have sex a lot happier than people who rarely have sex?

I appreciate your question, but it’s unfortunately incomplete.

Having consistent, regular sex doesn’t tell us anything about the people having that sex, the kind of sex they’re having, or their motivations.

Imagine you’re a lesbian raised in a conservative, homophobic, lesbophobic environment. Imagine also that your parents, family, and wider social circle indicate the unacceptability of same-sex romantic/sexual relationships. Imagine suppressing all thoughts of attraction to women and getting married to a man to appease everyone else around you.

Further imagine submitting to regularly scheduled sex (3–5 times a week) with the straight man that you married. The straight man might be happy, but the hidden lesbian out of necessity that you are most certainly is not.

Imagine you’re kinky but everyone around you thinks your preferences are sick and disgusting. Every partner you make love with offers you plenty of vanilla sex that does nothing for you. Happy yet?

Imagine that you’re a sex averse asexual in a very sexual world. Imagine everyone telling you you’re defective. You submit to regular sex with partners not because you really want to, but because you think you’re broken and need fixing. Are you happy?

Are people with high sexual libidos who regularly have sex a lot happier than people with high sexual libidos who rarely have sex?

Most likely so. Switch out the different kinds of people having that regular sex and see why the answer is far from a universal yes.