I've never really though of it that way, but I agree with you. I played Brag as a kid, poker seemed like hard work. and all the good brag players moved up to poker, so it was easier to earn the daily bread.
I didn't like to leave much money on the table, probably because I didn't want people to see how much I was winning, or that I had got. As an extension to your point. If you withdraw your winnings, then you have a new total for your stake, then your logic applies, even though the new stake includes previous winnings.