When can you negotiate as an individual?
Is the scenario you have in mind when there is an actual bidding war, when you go into a negotiation of salary with an actual offer from another firm, and neither one is offended enough to eliminate you from consideration?
How often does that happen to you and how often do you think it happens in general?
You don't actually need another job on hand to negotiate terms. It's also up to you what you want to haggle over, money or holiday, on call duties, etc.
I think the key is agency. If you have it, you can negotiate. If you're always in a terrible negotiating position like certain blue collar workers, it makes sense to be in a union.
Mind you, I'm not sure if would be bad for white collar workers to unionize. Doctors for instance are white collar and have unions.
You can always try. If you have always made market rate, then have you ever really negotiated anything? To benefit from negotiation skills, you would have to be making way below market and then somehow convince someone to pay you what others are making. And do it without flat out lying.
Just wondering, do you not negotiate? If so, you might be losing out on many multiples of your current compensation.
[0] https://www.kalzumeus.com/2012/01/23/salary-negotiation/
[1] https://github.com/vlvagerviwager/salary-negotiation-tech
No bidding war required. And nobody is offended. And it happens pretty often for white collar work in high demand industries.