If I were to evaluate exactly what is happening here based on the matrix (no matter how fallible) I've devised, it would look like this:
THE IYLLIC D&D SANDBOX
* Protagonist Agency for players is either (a) non-existent or (b) its relatively diffuse. In case (b) (where some or all of the PCs do have some kind of explicit dramatic need that play attempts to resolve), it is diffuse because (i) there are a huge number of dramatic needs within the sandbox and (ii) those must all be given expression through the GM such that (iii) there will be many, many moments of play that entirely unrelated to/not framed around resolving PC dramatic need. (i-iii) are necessary in concert so the dreaded "Rowboat World" doesn't materialize through play.
The "Side Quest" is the classical manifestation of this. Through the confluence of an accretion of "Sandbox Dramatic Needs" + "Side Quests (where resolution of those Setting Dramatic Needs are the focal point around which play orbits)" = "Rowboat World" is kept at bay.
For these games (like the one BRG seems to be representing), diffuse Protagonist Agency (which means both in total and for any given unit of play, PC Protagonist Agency is diminished or non-existent because resolution of Setting Dramatic Need is the apex play priority) is "a feature, not a bug."
BLADES IN THE DARK SANDBOX
* Protagonist Agency is central to every unit of play and the entirety of play in total. Although the Setting's Factions and the Setting itself has Protagonist Agency, the Players Protagonist Agency doesn't become diffuse. It just means that every moment of play will involve some collision of the Crew's dramatic needs with other Factions/Setting and, thus, play will orbit around the Crew's dramatic needs. There won't be "Side Quests" that are "PC dramatic need-neutral."
The skirmish over, let's call it, "Haunted Painting Incident" is a perfect example of this realized in play. Its also a perfect example of a player "grabbing The Situation Piece (and possibly grabbing the Setting Piece depending upon how the action resolution mechanics/fiction resolves)" in a way that isn't present in the Classic D&D Sandbox (again, hence the "scandal" over this).
Both Sandboxes.
Different approaches to dramatic needs (and therefore Protagonist Agency).
This is a HUGE pivot point of this conversation. One side is saying that (to take this exact example) that the Blades Sandbox approach invests the Players with more Protagonist Agency. The other side is either (a) disputing this differential in Protagonist Agency (for reasons that aren't clear to me...but I would definitely say that there is just some fundamental disagreement/misunderstanding of these concepts/paradigms that are stifling clarity and consensus) OR (b) the other side is saying that a Sandbox (or play in general) that orbits entirely around Player Protagonist Agency is not desirable for them.
To me (a) is not defensible, but (b) is 100 % defensible.
Further, I'd say that another HUGE pivot point of this conversation is a player "Grabbing Situation Piece or Setting Piece".
One side says that a more prolific ability for player to grab those pieces means (a) more breadth (at least) of Tactical and/or Strategic Agency and (through this) (b) an amplification of ability to positively resolve Protagonist Agency (because you can advocate harder and better for your dramatic need...your dramatic need doesn't become more relevant because its at optimum relevance already...but your ability to have your advocation for it result in positive affirmation becomes more potent).
The other side (a) disagrees with this (one reason is because of a misappropriation and misapplication of The Czege Principle...which the intent is to substantiate the claim "Tactical or Strategic Agency is subordinated by the Schrodinger's Painting") or (b) doesn't feel this is desirable.
To me (again), (a) is not defensible, but (b) is 100 % defensible.
Ironically (BRG would disagree with this I'm sure), this gets us right back to The Right to Dream essay on The Forge. (b) in both of the above (x is not desirable) is precisely because it makes those people feel like it negatively impacts their play priority of experiencing this particular variety of Sandbox play. And if it does negatively impact their experience, that is 100 % defensible! But just say that!
@hawkeyefan , you bet and sounds good!