I also think we're talking apples to oranges. A one person shop may approach contracts differently than a shop with 13 across 3 time zones.
How is it egotistical to say that you’re good enough at what you do that people will make their bureaucratic procedures go away to get you to work for them? It’s either true or it isn’t. The number of people who are literally the only person who can solve a given problem will always be minuscule but being one of the top five people in a very expensive niche is an achievable goal. Being the only one of those people with a public profile and a consulting practice is also achievable.
Think of academic expertise. I’m confident people go to Peter Norvig and ask him as an individual with incredibly deep, broad and publicly known Algorithms skills to do work for them and if they make it too bureaucratic he just declines the work. Likewise economists like Alvin Roth with mechanism design or other hairy, expensive and lucrative problems.
This model of being very good and being known to be very good works for individuals. I’d be shocked if there aren’t one man consulting shops that bill $1m a month, very expensive expertise exists, at a minimum in finance. They probably have a secretary but a principle plus minimal support staff consultancy.