I can't speak for P1 pedals but when I first read this thread I assumed the loss of data at the start referred to time lag of power meters reporting data - not so much the sleep-then-wakeup delay.
OK - these numbers are from road use not track: My P2M Type-S crank meter has chronic lag - like it starts reporting 4-5 secs after (I believe b/c it is slow to sense cadence). My Powertap G3 hub is better but still has 2-3 secs lag. My [non-scientific] 2016 SRM is around 1-2 secs as well.
So for standing start where the cadence is super low you'd only be able to see the first "average" of power number after the power meter trips/detects the second revolution (averaging torque between first trip of the cadence sensor and the second).
So... what I am trying this time is the Stages Track Dura-ace arm. It also reports torque w/ no lag at 64Hz on BLE to a phone app. It reports [average] power as well via ANT and BLE once it has detected circular velocity. For those first few seconds you can determine cadence (and thus power) from looking at the phase of course. When these efforts are closer to static efforts though I wonder if "power" is the right way to measure them. Obviously, once spinning then yes - power is the ultimate measure of work.
The main reason was that it was a quarter of the price of the SRM/PC8 setup
. Yes, it's left-only, but as a masters racer there's nothing actionable I am going to do about discovering a leg dominance (old dog, new tricks). Main goal is to use it as a pacing comparison tool so repeatability, instant response [and price!] were key.