You're doing that thing where you claim there's freedom of choice because you're ignoring the punishment inflicted on one choice.
The choice not to commit to a long-term relationship has had severe financial implications for centuries, especially if you are female. Until the invention of effective birth control, the choice to not have children meant giving up much of heterosexual sex.
While there are still problems, the ability to have healthy heterosexual sexual relationships without children is largely solved by modern birth control. But I would argue that the choice to not marry is still financially punished pretty severely, though perhaps not as much as in centuries past.
> There are people born rich enough to not have to work, but do they live a happy life by not working all the way?
You're asking this as if it's a rhetorical question, but it's not.
Being a rock climber, I've met plenty of Trustafarians who haven't done a lick of work in their lives, and are quite happy being skiing, surfing, or rock climbing bums.
The flipside, is when I've met people who tried not working and said they didn't like it, that has always been coupled with a profound lack of imagination or self-awareness. I distinctly remember a post on HN where someone took a week off and just played World of Warcraft for the entire week, and when he found this unfulfilling he concluded that not working wasn't for him. It should be no surprise that a lifestyle with no physical activity or direct human interaction is dissatisfying--this isn't proof that work is a necessary part of human happiness, it's just proof that giving up work without replacing it with something better doesn't succeed.