In my experience the people who describe themselves as “sex addicts” are people who were caught hurting their loved ones and trying to excuse their behavior, either socially (cheaters) or legally (rapists).

Somewhat adjacent, I have heard of people claiming “sex addiction” to pressure their partners into more sex than they would otherwise want. Apparently there’s a whole section of feminists who believe that “blue balls” is completely made up by men, because it’s really common for men to claim blue balls is a more serious issue than it is. I’ve had to explain to multiple women in my life that it is both real and just a minor inconvenience.

You’re not wrong about the religious zealots, I just wanted to bring up that there’s a TON of sex disinformation being spread by different people for different goals. And “sex addiction” is particularly ripe for such disinformation.