Except - There is an established baseline system pressure, the pressure switch is looking to maintain which I believe includes the entire braking system all the way back to the rear caliper. Hear me out.
After you shut the ignition off, over time the fluid slowly returns to the reservoir and system looses some pressure. During key on process, the (electric) booster runs topping up the accumulator and simultaneously building system pressure to make ready for brake assist.
Now what happens when you open a rear bleeder during the key-on initialization process? With foot off the pedal, the booster would continue to run and pump fluid until you close the bleeder to allow the system to achieve its initialization pressure right? When the pump is running it's creating/achieving its preset line system pressure with out depressing pedal. It makes sense to me that a worn brake hose would not hold line pressure as well as a new hose, and that a rubber reinforced hose would not hold pressure as well as braided stainless hose. Stainless braided hoses have greater burst ratings than standard rubber hoses. It makes sense (to me) that they don't expand as much under pressure either.
I had no other explanation for why the booster primed faster after installing stainless braided hoses. I had no leaking fluid or fittings that might cause longer priming time. After changing 15yr old brake hoses out to stainless reinforced braided hoses - I measured the booster priming time was reduced by 20-25%. Having bled the system twice before in past years my priming time always was typically in the high 30 second range: (36~ 38 seconds), now its consistently 28-29 seconds to prime. I attributed this to stainless hoses holding pressure better than worn standard rubber hoses- since nothing else changed in the braking system.
IDK seems plausible to me, but I could be wrong.