I think it's like Amdahl's Law. Programming is thinking followed by typing. If you spend half your time thinking and half your time typing, then doubling your typing speed will increase your programming speed by a third. But doubling it again will only increase your programming speed by a sixth, and even with infinite typing speed, you've only doubled your programming speed.
I'd like to think of a better analogy.
Typing in programming is like running in soccer.
It's definitely a problem if you type slowly or can't type for a long period of time.
Passing the certain speed and endurance, typing faster doesn't help much.
It's the same with soccer.