Though the rewards are great when it’s done well, period TV is difficult to pull off. For every “The Crown” or “The Americans,” shows that milk tension and drama out of their movement into a future we all know is coming, there are several less-well-remembered series that couldn’t make that leap. (A few of them premiered in the wake of “Mad Men.”) When we’re familiar not just with the setting but with what comes next for characters, seasons’ worth of investment through the infinitesimal movement of history can be a big ask. And the temptation to substitute easy cultural references for meaningful insight about the era is a big one.

That’s a problem facing “American Woman,” Paramount Network’s new comedy-drama hybrid set in the 1970s. The show, notionally based on the early life of “The Real Housewives of Beverly Hills” star Kyle Richards, positions her as one of the two children of “Bonnie Nolan,” a character based on Richards’s late mother, Kathleen. Bonnie, played by Alicia Silverstone, is a woman who’s happily traded away her independence and who comes to realize, when she discovers her husband has been cheating on her, that it was a bad deal. A divorcee handling family finances by herself for the first time ever, she steps into second-wave feminism without looking back.

Richards’s own family history, known to viewers of “The Real Housewives,” is far more interesting than what we get on “American Woman”; the show is surprisingly tame. The real Kathleen Richards raised her three daughters to be stars, and pushed all three into the entertainment industry at a young age. The only glimpse of that we get in the show’s early going is Bonnie’s fond reminiscence about studying acting before she was married. In her day-to-day life, Bonnie has had to perform wifehood until the part was cancelled; her post-divorce life is a series of put-ons, including an inner strength she doesn’t entirely feel. After yelling at two men tailing her car, she tells her daughters, “Let that be a lesson to you girls. Never let a man intimidate you under any circumstances. You always have to stand up for yourself.” She says it with a steeliness she evidently doesn’t come by naturally.

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Her posing her way towards independence is interesting enough, thanks in large part to Silverstone. And the ways in which her feminism differs from the sort practiced today are interesting, even as one has to puzzle that one out themselves; the show has no comment or point-of-view on that. But the show doesn’t give us nearly enough of whatever is the real Bonnie to make us understand why hers is a journey that deserves our time — let alone a title that positions her as an archetypal national figure. Much time is spent on subplots among her friends that are entirely disconnected from the story and offensively silly, to boot, like a disastrous one involving Mena Suvari and Cheyenne Jackson as a couple, in which she keeps missing ham-handedly obvious clues he’s gay. There’s a story to be told about the rise of gay culture in the 1970s, but treating it like an obstacle for a supporting character to overcome is badly underthought.

The show needed less of the “American” — obvious and pointed references to the ways in which society is changing — and a lot more of the “Woman.” Silverstone, charming and bubbly as ever, seems miscast as a trophy wife, a disconnect that ends up serving the show; her eventual freedom seems as though it were meant to be. But who is she? So consumed with positioning her in a fleeting historical moment, “American Woman” doesn’t bother finding out.

TV Review: “American Woman”Comedy series (12 episodes, 3 watched for review): The Paramount Network, Thurs. June 7, 10 p.m.Credits: Executive producers: John Wells, John Riggi, Alex Hardcastle.

Cast: Alicia Silverstone, Mena Suvari, Jennifer Bartels, Cheyenne Jackson.