I've started carrying 9/16" instead of 1" webbing, since it's so much easier to carry a 20ft length in a pack. Primarily, I use webbing for two things on caving trips: for constructing backup anchors for scary TAG bolts, and for when a handline is needed.
I do have one remaining question, however, and I can't seem to find the answer in any of my references. I know a W3P2 in 1" webbing -- Bluewater says 4,000# / 17.7 kN breaking strength on 1" -- is one of the strongest points in a system and perfectly suitable for use in single-anchor rigging. I can't remember how to calculate the strength of that anchor, however, so I can't determine what the strength of the same anchor is in 9/16" webbing.
Bluewater says 2,300# / 10.2 kN is the breaking strength of its 9/16" (15mm) tubular webbing. What, then, is the strength of a perfect-world Wrap 3 Pull 2 in 9/16" webbing, tied around a bedrock pillar or similar solutional feature?
Edit: I realize I could just email one of my rope nerd friends -- Tim White and Bill Putnam, I'm looking at you -- but it's more fun to ask the question publicly, and more useful to the caving community for the answer to be available on cavechat later.