Could be offering means they most likely won't. They'll give you the minimum they think you'll accept - if they care about the employee being you, specifically - and tell you to take it or leave it. All it's gonna accomplish is select for people of either gender who take what they're given and sit quietly instead of people of either gender who are looking to strike a mutually satisfactory deal.
This is not a progressive policy, that's a Gilded Era policy in futuristic clothing.
If they weren't willing to give people more then they wouldn't have had negotiations in the first place. If the base is $50,000 and half of people negotiated up to $54,000 a year, offering everyone $52,000 does not cost them anything and gives them this free publicity.
No. They are willing to go up the 4k because the alternative is that this particular candidate A walks away. Meanwhile candidate B is perfectly content with his 50k, because he was expecting 48k but got more.
If you offer 52k to everyone, all the employees who would have negotiated up to 54k are dissatisfied, whereas those who were content with 50k are, from the company's perspective, overpaid - since they would happily work for 2k less.
The company is willing to pay as much as 54k for an employee, because that's what their maximum value for an employee in a such and such position is, but they will try to minimise this value in their own self-interest. The employee is willing to accept as little as 54k, because that's the lower limit of his estimate of the value of his own work, but he will try to maximize this value in his own self-interest.
If we were to adjust your example, they'd have to give EVERYONE 54k, which costs them quite a bit. Only this way both groups are satisfied, but then the company is overpaying half of their employees 4k over what both parties would be satisfied with.