I wonder if there could be a way that a player's total number of KO wins could be displayed on his/her profile. Currently, it shows KO points but not tournament wins. There is a listing of the players with the highest number of wins, but if one is not in the top 150 or so and is not in a featured tournament in a given week, there is no way that I can see to find out how many tournaments he/she has won, is there?

I would not want mynKnockout wins on my profile page.

Any player can see how many wins they have by clicking on the "Most Wins" link on the Knockout page. The number of wins is listed at the top of the page.

http://www.funtrivia.com/knockout/mostwins.cfm

Inside the blue box, before the top 150 list starts it says -

The following chart displays the players who have the most weekly victories over the history of this game.
You have won X times.

Yes, I know that we can see our own information, but is it intentional that we can not see another player's total KO wins, or is that just an oversight?

I don't think it's an oversight.

Other than making picks in the KO Fantasy game, I can't think of a reason why I would need to know somebody else's win total.

And like you said, in that case the information is available in the featured tournament.