I completely fail to see what field size has to do with anything. ...
One thing it relates to is making sure the best potential performance gets the win. If you don't invite everyone, you can't be sure someone else wouldn't have gotten very lucky. Sure, the lower-rated players each have a small chance of winning, but there are more of them.
This goes hand-in-hand with the idea that Worlds should have enough rounds to make sure the best player wins. If there are more rounds to play, you can be more sure no one who was not invited would have stayed lucky long enough.
I simulated what would happen if a certain number of the top rated players were invited, and they played a certain number of rounds.
For example, say you want to be 99% sure the winner of the tournament includes the player who was going to have the best total score for the event.
You could invite 338 players (1001-rated and up) and pick a winner after one round, or
You could invite the top 49 players (1025+) and hold 8 rounds.
To look at it another way:
If you hold five rounds and invite 71 players (1020+), there is a 1.6% chance that someone you didn't invite would have had enough hot rounds in a row to be the winner.
If you hold five rounds and invite 190 players (1008+), there is less than a one-in-a-thousand chance that someone you didn't invite would have had enough hot rounds in a row to be the winner.