Two weeks ago, when news surfaced that DeMarcus Cousins was signing with the Warriors, critics of the NBA seized the chance to bemoan the rich getting richer. Their frustration was understandable: More than three months before its season opener, Golden State appeared to have quashed even the faintest hope of something resembling competitive balance.

All of that hysteria and hand-wringing, however, didn’t make the sight of Cousins posing Thursday morning with his new No. 0 Warriors jersey any less strange. It was visual proof that Golden State had done the seemingly impossible, adding one of the most dominant big men in the world to a team fresh off its third NBA title in four years.

The Warriors have bullied the competition with rookies and role players at center. With Cousins — a four-time All-Star, two-time All-NBA selection and one-time Olympic gold medalist — now manning the post, Golden State has destroyed any semblance of parity.

Asked during his introductory news conference Thursday about the notion that the Warriors are ruining the league, Cousins was bullish, declaring flatly that “I really don’t care.” And who can blame him? After reportedly not receiving a single contract offer in free agency, Cousins reverted to what he has called his “last resort” and phoned Golden State general manager Bob Myers.

For a player who had visions of inking a long-term max contract prior to his Achilles tear in January, the Warriors were the ideal backup plan.

A loaded roster ensures that Cousins, who signed a one-year deal for $5.3 million, can take all the time he needs to return to the court. Once fully healthy, he will play alongside friends Kevin Durant, Stephen Curry, Draymond Green and Klay Thompson without the mental burden of leadership.

Because head coach Steve Kerr doesn’t necessarily need a fifth All-Star, he can cater his system to utilize Cousins’ strengths and avoid his weaknesses. Unlike his seven-year run with Sacramento, when he was forced to shoulder a heavy load whenever he stepped on the floor, Cousins will have the luxury of fitting into a team framework.

In addition to honing his game and recovering from injury, he joined Golden State to resuscitate his reputation. Cousins, for all of his immense talent, is one of the NBA’s most polarizing players. Given his run-ins with coaches, referees and reporters, it was no surprise that some teams refused to pursue Cousins under any circumstances.

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The Warriors subscribe to the philosophy that, when surrounded by selfless teammates and coaches, any player can thrive. It is why they took fliers in recent years on JaVale McGee, Matt Barnes and Nick Young. Because his infamous tantrums won’t be tolerated in a locker room built on joy and winning, Cousins would risk ostracizing himself by slipping into bad habits.

Though he is 6-foot-11, 270 pounds with a soft touch around the rim and a feathery jumper, Cousins has yet to play in a playoff game. His tenure with the Kings was defined by drama and trips to the lottery. After Cousins was traded to New Orleans at the 2017 deadline, the Pelicans failed to make the postseason. They regrouped in the wake of his season-ending Achilles tear on Jan. 26, ratcheted up the tempo and reached the second round of the playoffs.

When Cousins called earlier this month and asked for a contract, Myers told him, “You deserve to play in the playoffs.” With the Warriors, he will get something even better: a shot at a championship.

“Just the chance to play for a winning culture,” Cousins said of why he signed with Golden State. “I also have a chance to play with some of the most talented players of this era. So, those two things alone, that pretty much sums it up.”

In Cousins, Golden State has the skilled center it has long lacked. The defensive attention Curry, Durant and Thompson command should allow him space to operate. Kerr already has ideas for how to roll the offense through Cousins in the low post, though Myers insists that they will still encourage him to shoot the occasional three-pointer.

Cousins must prove that he won’t be a liability in the Warriors’ switch-heavy defensive system. If nothing else, he has the size and lateral quickness to spell Green and Durant from time to time on tougher defensive assignments. It also helps that he matches up well with two centers Golden State could face in the 2019 NBA Finals, Philadelphia’s Joel Embiid and Boston’s Al Horford.

More Information Cousins’ NBA stats Year Team Pts Reb 2010-11 SAC 14.1 8.6 2011-12 SAC 18.1 11.0 2012-13 SAC 17.1 9.9 2013-14 SAC 22.7 11.7 2014-15 SAC 24.1 12.7 2015-16 SAC 26.9 11.5 2016-17 SAC* 27.0 11.0 2017-18 N.O. 25.2 12.9 Totals 21.5 11.0 * Traded from Sacramento to New Orleans mid-season Carmelo traded: Hawks acquire Anthony, are expected to waive him. B6

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Perhaps the biggest benefit of Cousins’ arrival, however, deals more with motivation than X’s and O’s.

Last season, after making only minor tweaks to the fringes of their rotation, the Warriors struggled with complacency before eventually sweeping Cleveland in the Finals. By easing Cousins into its system, Golden State should guard against the doldrums that come with trying to play deep into June for the fifth straight year.

“I’m looking forward to seeing how he acclimates to us,” Myers said. “Yeah, there’s going to be some moments, but we might need some moments. We need something different. Even though we won and finished the way we wanted to finish, there was some staleness to our season. I don’t think it’s boring with this guy.”

The biggest drawback to Cousins’ addition is that it will probably be brief. If all goes according to plan, he will hit free agency next summer with a shot at quadrupling his annual salary elsewhere.

Such realities weren’t the Warriors’ concern Thursday, however. While much of the league eulogizes the end to competitive balance, Golden State is still reveling in yet another free-agency coup.

“You never know what’s going to happen in free agency,” Myers said with a smile. “To have a guy like DeMarcus get on board with our championship pursuit, it’s fantastic for our team, our organization, our city.”

Connor Letourneau is a San Francisco Chronicle staff writer. Email: cletourneau@sfchronicle.com Twitter: @Con_Chron