Seven months is a long time
That's the approximate time to travel to Mars — seven months. That's a long time! A lot of things can happen in seven months and any one of them could rationalize a larger crew.
Maintenance: One of my favorite movie moments comes from K-19: The Widowmaker when, during a missile launch simulation, a burn-out occurs. When some bureaucrat demands to know the name of the person responsible, Liam Neeson responds, "Why would I know the name of the jackass that supplied a 30 kopeck insulator to do a 50 kopeck job?" Think that's unreasonable? Think "Apollo 13." No ship is perfect, and no space agency would send a ship on a seven month cruise without an ample supply of spare parts and the people to maintain it. (Why don't they do that today? For one thing, the Space Shuttle's longest mission was only a bit more than 17.5 days.)
Emotional Health: Even the most introverted person needs occasional human contact. Emotional stress on such a long journey would be enormous. And you'd be surprised how easy it is to fashion something into the shape of an axe. You might not justify 70 people this way, but you'd justify a few more than 3-5.1 (This builds on @KerAvon2055's answer, which I upvoted. If the ship can be flown by three people, you'd want at least twelve because someone must always be monitoring the ship and that would get incredibly tedious.2)
Economy of Scale: When the world's national space agencies formed the Global Space Initiative (GSI) in 2031, they realized that economy of scale was very much their friend. The Mars mission ship was already humongous due to basic life support, power, and engines. Not to mention the cargo of equipment to be used on Mars. But that's inefficient! Why not use all that equipment en route, and even add a bit more to do cool things like analyze Space in transit? Need a few more scientists or engineers for that? No problem! Add a bit more living space, a little bit more fuel, food, and oxygen and we're good to go! (This builds on @Thorne's answer, which I upvoted. While governments tend to spend wastefully, NASA and other space agencies have demonstrated the ability to make the most out of the little they get. There would be a fair amount of pressure to make those seven months very, very productive.)
Supporting Labor: The more people you have, the more you need supporting labor. Cooks, janitors, admins (of varying types). It's a nice theory that you could get away with just a few people on that ship, but every person you add means you need to help them live their lives. Remember when three people for seven months would really need to be twelve? Now you need fourteen (at least), two people to care for the other people who need their chance to do their jobs, eat, sleep, and relax. The compounding of labor adds up quickly, otherwise you need to deal with the stress of individuals doing multiple jobs: navigation and cooking, communications and cleaning the bathrooms (so to speak). There's always a price to be paid. If you send 70 people to Mars, you can bet that 15 of them are supporting personnel — the people you never see in the movies because, apparently in Hollywood, space ships clean and cook for you.3
Political Intrigue: OK, the GSI wasn't created in 2031. In fact, due to a massive international financial collapse in 2029, the only space agency left operating is the South African National Space Agency — but that hasn't dampened all other nations' hopes of working in space! The competition to get on that Mars mission is fierce, and South Africa isn't a fool. Rather than risk being bombed by someone for not letting their
pet favorite astronaut join the crew, they simply built a bigger ship (with a bit of a donation from those cash-strapped nations) and loaded not one, but ten full crews onto it. One for each participating nation. And, yup, by treaty, each crew gets its turn at the proverbial wheel.4
Biological Necessity: Ten years after the COVID-19 panic of 2020 the world is finally vaccinated — but politicians and scientists who spent the decade calming fears know an ugly truth: that virus can mutate a lot more than the public was ever led to believe. Those 70 people aren't on that ship because there's actually 70 jobs that need to be done, they're there because the mutation and mortality rate simulations suggest that when the ship re-enters Earth's orbit two years later, there will only be three living people on board.
1 And if Hollywood has proven anything, it's that there's always an axe. NASA could go out of its way to be sure there were no axes on the ship and someone would find one anyway. Call it karma, call it fate (call the Ghostbusters!) but 210 days into the 215 day mission, someone would go ape berserk and suddenly there'll be an axe. There's always an axe!
2 You might consider reading Frank Herbert's Destination: Void. He did a good job of imagining what space flight might be like when there's too much to do.
3 You know, I get the idea of Star Trek replicators, but they never show anyone actually cleaning. Do you have any idea how many people would be necessary to clean a ship the size of Enterprise?
4 It's a mistake to believe that the crew must have mission-related reasons to be on the ship. Frankly, you could justify a dozen people as tourists, the launching space agency having used the funds from the over-priced tickets to pay for the mission. 2001's first space tourist Dennis Tito started a very real trend that you could use.