9 other people is the opposite of bad reasoning.
When considering there's 10 people in each game rather than 1: every time you feel like dodging means you're going to have roughly 9 times as many games dodged if everyone else dodges the same amount on a whim.
Also: considering there's 10 people per game: waiting until the last second in blind pick and dodging means you can waste a collective 18 minutes of other people's time.
Waiting until the last second to dodge in ranked (which can take exactly 8 minutes with 16 30 second intervals for each pick and ban), means you're wasting up to a collective 72 minutes of other people's time, more often than not it's closer to 45 minutes: which is still longer than an average game.
there are (apparently) 40 million people playing this game.
And again: you're not the only person in 40 million capable of dodging.
All 40 million of those people can dodge, and if the game is in a state where you feel dodging 1/20 games is appropriate: it's quite likely 40 million other people will feel dodging 1/20 games is appropriate.
In which case 95%^10 = ~60%, or only 3/5 games actually make it past the pick phase and start.
Another way of saying that is queue times and the pick/ban phase is effectivly 40% longer because of a 1/20 chance every player will dodge.