"There has to be a round in the chamber for a round to be fired" seems sort of tautological if I'm being honest.

Very, very few serious people would argue that anyone carrying a firearm should carry it without a round in the chamber. Yes, "Israeli carry" is a thing, but is almost entirely endorsed simply as a training carry-over from a time when people carried different weapons of widely varying mechanical safety features in a very unique high-threat environment.

If you're carrying a firearm professionally, or in the US "recreationally" for personal protection, carrying without a round in the chamber will be seen by most people as a pretty stupid decision.

As a Sig 320 owner, and someone that knows at least 3 other sig 320 owners, I disagree. None of us ever carry our weapon chambered. I probably know 10+ guys that own guns, including a few police officers, and I'm going to ask the officers about this because honestly, I would be surprised if they even carried their weapons chambered.

I wouldn't carry with a round in the chamber if I carried a 320 either.

There is zero chance that those police carry un-chambered

Your experience is an outlier.

My father was taught to use condition 3 carry (unloaded chamber) with a 1911 in the 1970's US Navy. It all depends on circumstances.

You might not, but this is exactly how a pistol like this should be carried.

The usual response to this is that if you don't carry with a round in the chamber, you could spend the rest of your life racking the slide.

That's exactly how guns are supposed to be carried. Exceptions exist, but if you're carrying a gun you ought to be ready to use it.