@Kenan Toast of the Town is not a sandbox. Obviously, I'm painfully familiar with sandboxes. They are not intrinsically low-trust, but all of the many sandboxes I've studied have been either low-trust or DnD.
There is no storyline in HTT play. At no point in HTT does the GM, or the players, or the PCs, create a storyline.
I'm glad you enjoyed reading Toast, but I feel you've mischaracterized it.