Just out of curiosity, in what decade did the training you underwent take place? I'm not trying to be snotty, I'm really curious- there was a pretty significant shift during the latter part of the last century, when Cooper started popularizing the 1911, and arguing against point shooting. Prior to that, I suspect most people would have agreed with your position.
Now, the overwhelming majority of trainers (rightly or wrongly) would disagree.
I wonder if what we have is merely a generational difference in training?
It could be, but I doubt it. I think I would rather error on the side of general safety. The time it takes to arm an automatic is insignificant, there just aren't the fun old fast-draw duels like there were in the old days. However, we all know that an armed gun will occassionally discharge when dropped, bumped or when going about life (like in a theater). There is no need for anyone to carry a pistol with a chambered round. It's like running with scissors, it's begging for an 'accident'.
One can make a strong case for NOT carrying a weapon with a chambered a round (accidental discharge being primary, time savings being near zero). I have talked with several cops, and I have never heard one say "I drew my gun and immediately began to fire". If you feel you are in danger, draw your gun and arm it. In the case of Houston, TX TWO officers had a suspect unarm them, and shoot a total of 4 officers just about a month ago. If the suspect had to arm the pistol, there is at least a 50% chance that 1 of the 3 wounded officers could have shot him. Therefore, I cannot make an arguement to always carry a pistol with round chambered. It's an accident just waiting to happen.