It keeps things in conflict with interesting, dynamic things occurring and corresponding decisions by the players to be made. Imagine if whatever D&D you're used to playing had an exciting Complications Deck that changed the situation dynamically on the heavy bulk of successful rolls you made. You draw a card and something interesting happens where a new branch on a decision tree emerges, you have to deal with a new problem, decide on a trade-off, pay a cost for a benefit etc. That is the deal.
As a threshold matter, I'd prefer the complicataion be chosen by the DM rather than by drawing a card. I trust an experienced DM to more reliably produce enjoyable complications suited to the group (and their current mood) than a random choice being picked from a list drawn up in advance. For the same reasons, I rarely use random treasure generation, and also don't use wandering monsters (the closest I come is an ability check to bypass a known threat in an area).
But I also wouldn't want such complications to emerge on the heavy bulk of rolls. Instead I would want the frequency of such complications (as a percentage of die rolls) to closely reflect the choices made by the players. If they find a strategy to achieve their objectives that plays to their strengths (either on the character sheet or in-game resources and advantages), I would expect complications arising from check results to occur less frequently, on average, than for a party running greater risks, either through choice or desperation.
Also, I don't understand how this...
And I don't want to get into subjective vs objective DCs, but yes, like 4e the system's target numbers don't move. 6- and you fail and mark xp. 7-9 (as above). 10+ and you get what you want.
...and this...
If you just go with the most basic fundamental part (2/3 of all Move outcomes resulting in success with costs/complications/hard bargains/ugly choices)
...are compatabile with the bolded parts of this...
Finally, the players have a staggering amount of agency in the game. Just to start with your question, yes a player's choices significantly affect both the trajectory of play and their odds of success on any given move:
...and this...
6) The players choose how they strategically deal with situations and, of course, make Moves at the tactical level which engage their PC build resources that affect the potential outcome of any given roll.
If the target number to roll on the die/dice is always the same, how can the player's choices or the abilities on the character's sheet affect the probability of success?
The first two quotes suggest that no matter what the player's plan is, the odds of complications are fixed. The second two quotes suggest the odds of complications are not fixed. I'm sure I'm missing some mechanical element that makes those non-contradictory, but I don't know what it might be.
You mentioned the 2/3 was an average, but to be sufficient to resolve the apparent contradiction would require either that 1) making choices or using an ability to decrease the odds of complications on one roll necessarily increases the odds for complications on future rolls, or that 2) the frequency with which a player can change the odds is so limited as to not heavily affect the average. Both options would imply that the players only have tactical agency, not strategic agency, since in either case they lack the ability to affect the long-run average.
My apologies for the plethora of questions. I thought I'd inferred the gist of DW from the earlier discussion, but apparently I was wrong, so now I'm trying to clear up my confusion in arrears.