That makes it sound like beams are shared by ground stations. Why would the satellite bother doing that when it can use a phased array to instantaneously shape a beam specific to each ground station that it wants to reach? If the satellite is sending the number 4 to ground station A, then it sends the 4 to ground station A with its own beam. Then it has a 6 to send to B, so it sends that directly at B. Why create a 'static' beam that covers both A and B and send 4 to A and 6 to B?
Starlink system capability, at least for the most part, is limited by the aggregate capacity of the user beams, not the gateway beams. The user beams are indeed formed by a phased array (the gateway beams are not); the size/angle of each beam is almost exclusively a function of the number of elements in the array, which is almost exclusively a function of the physical size/area of the array. I'm not sure exactly where SX is right now, but I'd guess each sat can pretty much form a beam 'grid' with 5000 or so cells. So...the 350km sat can form the same 5000 (or whatever beams) in a much smaller area. It should be noted that what an increasing number of beams brings to the table is the ability to reuse spectrum more often within the total footprint of the satellite--that's the real technical enabler behind the increased density/capacity description from above.
It seems like you only gain in bandwidth if you increase the number of satellites because each one represents an available data cable that a ground station can connect to. The ground stations in view of a satellite must share the wire while the satellite is in view.
The reason this doesn't math out is because capacity is first and foremost a function of regulated power on the ground. It doesn't matter if you have 1 or 100 satellites putting power down over an area; if beam size is the same and thus total number of beams in the area is the same, the max capacity (assuming the one sat is capable power-wise) is the same.
It certainly is true that a lower satellite with a smaller total coverage area results in the constellation needing more satellites to provide an equivalent level of coverage [to higher sats], I that's where you're thinking. Once that metric is satisfied however, more satellites can't actually add capacity. (More sats adds system upside in the form of redundancy, for things like dwindling energy budgets and failures)