They really only need to pay you market to keep you. (But if your performance is above-average they should pay you above-average.) It is hard for an above-average employee to get an above-market salary when switching, because most employers don't have their interview process set up for that.
Remember that switching jobs is also risky for the employee, so switching for the same salary doesn't make sense unless your current environment is bad/toxic. I've had the old bait-and-switch a couple of times, where a job didn't turn out to be what I thought it would be. I've also had jobs where my boss wasn't the person I thought it would be when I was interviewing, and then my actual boss decided he didn't want to work with me.
The key is that if you're above-average for a given market, you're average in a higher-valued market. All you need is a single job offer in that higher market to force your current employer's hand one way or the other. When you are the product on offer, the employer doesn't get to define what markets you're available to; they have to play the hand you deal.
This applies geographically, as well - if an employer says "Well, they might be paying that rate in SV, but round here..." then you need to be applying for remote positions. They don't get to opt out of that market either.
Actually you can always play insane and demand a higher than market rate from your current employer - it will cost them a lot to replace you and train a replacement. The only problem is to find a way to get them to believe you are "insane".
Remember that switching jobs is also risky for the employee, so switching for the same salary doesn't make sense unless your current environment is bad/toxic. I've had the old bait-and-switch a couple of times, where a job didn't turn out to be what I thought it would be. I've also had jobs where my boss wasn't the person I thought it would be when I was interviewing, and then my actual boss decided he didn't want to work with me.