I'm not read enough to understand exactly how the Kessler Syndrome scenario cstross proposes would interact with GPS, but significantly naval spending by the Superpowers is the big powers is the major effect I can easily see. When you have to protect undersea communication lines for military command and control (assuming the Kessler Syndrome would be a convenient way for hostile nations to launch attacks against other nation's orbital assets), meaning drone warfare becomes untenable outside a direct LOS engagement if undersea lines are not secured.
I also think there would be a major issue with weather satellites and prediction, causing a significant investment to be made in weather radar and alternative weather prediction and monitoring strategies.
> I'm not read enough to understand exactly how the Kessler Syndrome scenario cstross proposes would interact with GPS
GPS needs 24 satellites to function as planned. (It might work with less, but 12 seem to be the minimum under optimal conditions).
• If a Kessler cascade happens in the GPS satellites' orbits, it will rapidly disable existing GPS satellites, and deny access to said orbits for new satellites. Replacements could be launched into safe orbits, but this will likely take years, and those orbits will have a faster decay rate and less visibility (so you'd need even more satellites).
• A Kessler cascade in LEO will likely deny access to higher orbits, so while existing GPS satellites will continue to function, they cannot be feasibly replaced once their 10-30 years life span is exhausted.
I also think there would be a major issue with weather satellites and prediction, causing a significant investment to be made in weather radar and alternative weather prediction and monitoring strategies.