I think this is faulty reasoning. Yes, the amount of knowledge has increased exponentially but the efficiency one can access that has also increased tremendously. Not only that, free and good learning materials/tutorials/lecture videos, etc. abound. So, in 1800 you could get expertise by reading a few books (or one, e.g. Heaviside spent years holed up with Maxwell's book to come up with his wonderful insights, there were no other books) but to find them was no easy matter.

The 10-year expertise rule is also sometimes misused. That rule applies to expertise of a certain kind (i.e. sending telegraph messages, playing tennis, writing code) and may not be applicable when simple learning is involved. Also, it assumes that one wants to be world-class in the chosen expertise area. Therefore, I think it's a very loose upper bound on the time.

Experience this yourself: Buy Penrose's The Road to Reality and give yourself 6 months. At the end, you'll be at a mid-masters level in Physics (admittedly concentrated on a few topics). Or Feynman's QED book for a similar effect in a different physics area. Or learn how to read Ancient Greek (in college you are expected to read Plato in the third semester! No after then years.)

Another example: My son was having a lot of ear infections and his doctor wanted to get an ear tube put in. After focused reading on the Web for 2-3 days, I felt that I had almost as much knowledge as her on this narrow topic. I even had access to recent research on the subject she didn't know about. Try doing that in the 1800s.

Today, universities turn out middle-class PhDs by the thousand, each grinding away in their own tiny corner of academia. The chance is rather small that someone who hasn't dedicated their life to an area can be competitive with the legions of specialists who have.

Takeaway for me: screw standing out on a global or historical scale. Do good work and get creative and you might get lucky, but first you gotta do the good work and get creative.