That's not actually the problem. The satellite footprint is >1000km across, and they can just launch more satellites to serve more customers. They would happily launch enough sats to serve every customer in the world if that was the only problem.
The issue is rather bandwidth density on the ground. Starlink achieves it's high system capacity by SDMA. That is, every antenna, both on the ground and on the satellites, is very highly directional, and they can have a single satellite talking to many customers on the ground at the same time on the same frequency, so long as the angles between each customer are large enough. The ground antennas are, for cost and physical size reasons, less capable of distinguishing between different directions than the satellite antennas, and can only do so if the angle between the transmission origins is ~>10°. This means that any location on the ground (iirc with a spot size of ~10km or so) can only handle a few dozen simultaneous beams, no matter how many satellites you have up there.
https://www.reddit.com/r/Starlink/wiki/index#wiki_-_will_sta...
That links to two timestamps in a 47 minute livestream by Elon Musk. There's no canonical answer on starlink.com.... because that site has basically no info on it.
If Starlink had come out saying they wanted to provide access to everyone the telecos would have came in and said Starlink has to also allow reselling of access like how they're forced to (at least in Canada).
It is a lot easier to show up and just tell everyone, "Remember how rural areas aren't profitable for you? No worries, we'll take this trouble from you."
From what I've read, they had a lot more people sign up for beta testing than they needed, so some people just didn't get the invite.