Except this misses the fact that negotiating for your own pay raise is now suddenly harder. Suppose there's a company with 100 non-supervisory employees, each of which $200k worth of value for the company, gets paid $100k. Under a regime where everyone's pay is automatically bumped up to the highest rate, if you're trying to negotiate a $10k raise for yourself, you're actually negotiating for the company to part with $1M ($10k * 1000 employees). Without such a regime, a negotiated $10k raise for yourself only costs the company $10k. Obviously negotiating in the latter situation would be easier to pull off.
Of course, the real world is more complicated than this, because the union can hire trained negotiators or whatever, but your simplistic model of "max(individual rate, group rate) so everyone wins" makes no sense.
Even a business like Apple has some number that is the most it can pay to all of its employees. And if there is a maximum, then that means it can be divided any number of ways.
There isn't some fixed bag of money $X that gets distributed to employees, where X is uninfluenced by the market. If the labor market happened to change such that X must be more, companies would have to pay X or do without some employees.
Keep going along this track and “max(individual rate, group rate)” will break down as you winnow down the definition of group.
Bad negotiator? Anxious? A woman? Congratulations! You're probably doing better than you could on your own.
Amazing negotiator? Could sell ACs in Alaska? Congratulations! You get all the fruits of your labor and your new coworkers immediately love you.
I think what messes people up isn't that they think their temporarily embarrassed millionaires, but that their temporarily undiscovered principal engineers who deserve more money for pulling the same cards as everyone else on the team.