1. As another commenter pointed out, most jobs are in "at-will" states.
2. Many companies require arbitration instead of litigation to settle any disputes as a requirement of employment.
3. It's just as expensive for the fired employee, probably more so, since if you litigate, you're unlikely to ever work again.
The cost is also not that high in non-at-will states, since there's typically a 3-6 month "evaluation" period where no paper trail is required.
There’s a lot of political bodies focused on playing up the idea that women and minorities are this big bad wolf suing legitimate businesses left and right over nothing, and winning. But it’s a largely fabricated narrative created by people trying to turn the leftist identitity politics arguments into a quagmire by “both sides!”ing the situation.
In reality there’s a substantial burden of proof for someone to win a wrongful termination suit.
The simple explanation is that it's really expensive to fire someone without cause. It takes months because the company has to produce a paper trail proving they fired the person for a valid reason to protect themselves from litigation. That's months of paying an individual who may be incompetent or toxic, months of paying people who put together the paper trail, all the morale damage the individual causes, the damage that might arise from firing someone, even if it's someone no one really liked.
All of those things are costly, probably much more costly than not hiring the right candidate. At least so the reasoning goes.