A real example that I've seen: two workers work for the same employer and have been given offers from other companies located in a different State. The single mother in the group had significantly less leverage because she (and presumably her employer) knew she couldn't move without potentially affecting the custody of her kids. She didn't get a raise.
Or to extend your example, someone living in KC has less leverage because they cannot use the COL argument to justify higher pay. If I'm being courted by an employer to move, you better believe I'm building COL considerations into my overall salary ask.
This just doesn't exist, not even in a hand-wavy rhetorical sense.
Are they paying 250k base in London? They weren't a few years back, and therefore they pay based on the market.
The London thing is even funnier because they claim to want top talent, but refuse to benchmark against actual top-talent companies in London (i.e. finance).
It's just nonsense, and if some of this gets disrupted by remote work then I (as someone getting screwed by the current system) will be all for it.
Take 2 people of equal skill, experience, and negotiating prowess. One lives in SF, another in Kansas City. Both apply to the same remote position for a SF-based company. The company will always take the one in KC. I don't see how negotiation skill has a role in this. Unless there are people out there who have successfully negotiated a SF-level salary while living somewhere like Kansas, but I haven't heard about it.