This is actually a very interesting suggestion. I am not sure that very many people within this community are familiar with the concept of "Ladder matches", and may be confusing the term "Ladder" with the physical ladders that exist in the game.
I had some experience with this in another online gaming community a long time ago and it was pretty successful for a short while. There were even special websites at the time set up for managing the matches, inputting the results, automatically adjusting the ladder rankings, etc. It's been a while, but I assume such things still exist.
My very vague recollection of how this works is that all of the players are ranked from 1st to whatever. Then, a player can challenge another player who is within a few rungs of them on the ladder and that player would be forced to accept the challenge. If the lower ranked player wins the match, he moves up a few notches on the ladder and the other player would move down a few notches on the ladder according to some set formula.
By far the biggest challenge with something like this is player availability and willingness to try to coordinate their schedules for the simultaneous start. It could be that we'd need a 2 - 4 week window for a player to agree to play once challenged since real life can easily force us away from the hobby for weeks at a time. All sorts of forfeiting and match avoidance rules would need to be hashed out, etc. Like I said before though, I think there are relatively "standard" ways that all of these issues are handled as set up by one of these websites who specializes in this sort of thing.
If the OP can post a link to such a website or to more detailed information about how this works I think that would be helpful to people. If I can come across the information that I am thinking of, I will post a link in this thread as well.