There is something related to effort as well. When i was studying in korea at a point, there was a small 9x9 board tournament in the school.
After playing move 2, i realized that i had become strong enugh to read the game until the outcome was decided. Its not like i was 9x9 perfect player, but i had enough reading power to count the score with an empty board.
It would take me 20-30 minutes to finish the game. I won that small tournament knowing exactly the score of each game and when i was losing and turned around games. After that, i never played 9x9 again. I dont like it, becuase i know i can lplay very well, but its a tremendous effort that i dont want to do.
A professional has to save face against an amateur, because losing would affect his reputation, his mindset etc. So a pro would be more reluctant to play a strong player than a weak player, where he might be able to use less effort.
A short way of putting it: professionals dont play for fun, so why would they play for free for anyone?