Phased arrays are not magic, but they are better than you make them sound like. When the directivity of the beam scales logarithmically with the element count,

Phased arrays are not magic, but they are better than you make them sound like. When the directivity of the beam scales logarithmically with the element count, it just means you need a whole lot of elements. The beam sizes are in the FCC filings, and they will be able to fully re-use the frequencies for ground stations that are >20km apart. (Not with the same satellite, you want adjacent beam spots on the ground to come from different satellites, but with literally hundreds above you at any time, that's not a problem.) Availability of bandwidth does not really limit them until the satellite counts are up to really hilarious numbers. The aggregate throughput numbers in the paper you linked are correct, for the initial FCC filing. Since then they have multiplied the size of the constellation by ~7 and the throughput per satellite by ~3 (for 2.0 satellites). (ISL's are still missing, though.)