There's a myth that someone who puts on their first dollar this week has an advantage over someone who has been paying in all year. Those first-timers are more likely to just increase the amount of the prize than to steal it. Enough more likely to make it fair.
If you want to be really fair, you would charge more for those who have a better chance of making an ace. Charge 900 rated players $1.00, then subtract (or add) 10 cents for every 50 points of rating.
850 = $0.90
900 = $1.00
950 = $1.10
1000 = $1.20
But, as you can see, $1 across the board is close enough.