So, this is non-intuitive to me, especially if you're the kind of person who generally avoids cross-chaining anyway. With a triple, the big chainring will be closer then a double to being in-line with the small cogs on the cassette, which are the ones you'd normally use with the big chainring anyway. Similarly, the small chainring on the triple will be closer than the small chainring on a double to being in-line with the large cogs in the rear. And, the middle chainring will be in-line with the middle cog, so you'd get to go further up or down the rear cassette than on either of the chainrings on the double.

I ride a compact double. It shifts fine. If I go to the third smallest cog, or less, with the small chainring, I need to click the front brifter one notch from the stop to avoid hitting the derailleur. If I cross-chain small to small, the chain barely touches the big chainring, but enough to make a slight noise. Since the difference between adjacent chainrings is less on the triple, that's less likely to happen, right?

And with a triple, you're less likely to cross-chain. You essentially have a chainring for hills, a chainring for flats, and a chainring for descents. You won't be tempted to go big to big as you sometime are with a double: you'll get into the middle chainring quite a bit sooner.

Maybe I used the wrong search terms here, but I haven't seen the simple geometry of the situations explained to my satisfaction. Thanks in advance for your explanations.