I really thought Globalstar was a LEO constellation, but the coverage map makes it look a lot more like a fixed geosynchronous fleet with beams. What am I missing?
It's LEO. The coverage map isn't restricted upon your device seeing satellites. You could see them anywhere on the planet.
A caveat is that Globalstar's orbits
intentionally biases below the 70th parallel. By ignoring the poles they increase the coverage inside of the parallels. It's about most efficiently covering the planet with a finite number of satellites that have a specific transit. There's just not as many users who might benefit so it's a cost-benefit business decision when they designed the system. They get better coverage over the rest of the planet with 48 satellites instead of 66 that Iridium uses.
The reason for the terrestial bias is Globalstar is a bent pipe, which means your device is relayed by the satellite directly to a ground station. Those ground stations are in fixed locations near the ocean but always on land. If you were to stand at one of their ground stations and measure 876 miles above the horizon, that is the limit to their view of that satellite. If you draw a line returning to the Earth on the other side of the link but continuing in that same horizontal line that's the maximum distance from any point on land they can support a communication path.
Now the Iridium satellites talk to each other and can bounce your link around in space until it hits a satellite with a view of a ground station. Which is why they aren't limited to a distance from land. Their constellation can adjust for the satellite you're seeing on a ship or land to find a path back to a ground station.
The problem is all that bouncing means not only do all the satellites need to see each other but they also need to find ones that see a ground station and another that sees you, too. Remember even if the station and you are both fixed all the satellites are moving so they hand off the uplink and downlink as they transit, Iridium's approach requires each satellite to additionally hand off the space link, too. All of this assumes a lot more things have to work right and many more hand-offs, which doesn't always happen so they'll get somewhat more dropped calls, harder to initiate a call, less bandwidth.
Each approach has benefit and issues, it's not one is always better than the other. Globalstar just relies more heavily on a ground network with fewer satellites and less complexity in space than Iridium. OTOH, it's a lot easier to fix stuff on the ground if it hiccups. To get full coverage on the ocean Iridium had to do it that way.
