Now that they've learned the system, it might go faster in the future, but it's really up to the players, case by case. Sometimes we'll want to skim through it; sometimes we'll want to play out longer scenes in downtime.
It's my GMing style, yeah, but it's also encoded into the game system of Blades. There are lots of judgment calls (like every RPG) and the distribution of authority on those calls is more group-based than GM-centric, by the rules.
In the future, we'll probably gloss over his wins and losses at the table -- it's the thrill of gambling that satisfies his vice. But I might offer him a true gamble now and then if he wants to. Put up an ante and roll a die to see if he loses, wins, or pushes.