GJM -- mostly the understanding is that under pressure you fire faster and worse than you do in practice.
How much training, and how many times you've been in a similar situation will level that out.
But for the majority of high end user groups - accuracy above all else is stressed.
The other understanding is that gunfighting is just part of the job, medical, comms, breaching, etc all take time too. Only so many hours in the day.
I will say though that in the last 5 or so years speed has come up greatly
A good carbine/pistol test - is Jason Falla's (Redback One) Operator Readiness Test.
https://www.youtube.com/watch?v=R57R5Iz2ndo
Which has speed, accuracy, reload, transitions etc built in. It's sort of like a carbine added to a FAST - but in full mission gear.