To begin with, Starlink sats have a mass of ~260kg not 227kg.
Secondly, the reusable Falcon 9 LEO payload has a limit of around ~15600kg; the 22,800kg payload is for expendable Falcon 9.
60sats*260kg = 15600kg.
This mass limitation can be verified in the fact that for Starlink L8, SpaceX had to remove 2 Starlink sats to add 3 Planetlabs Skysat with a mass of 110kg each, which produced a payload mass of 15410kg. (an additional starlink sat would've pushed the mass to 15670kg)
So basically SpaceX launch 60 at a time because of mass limitations.
The other main limitation is fairing volume, because 60 sats is likely at the limit of the fairing volume.
But if they were develop a bigger fairing, would they launch on an expendable Falcon 9, as it would be able to deliver more sats to orbit? No, because it's cheaper for SpaceX to launch in reusable mode. Current
estimates put the internal cost of an expendable Falcon 9 launch at ~50 mil US vs the reusable Falcon 9 at a cost of ~30mil US. This puts the launch cost per sat at 570,000 US/sat for expendable and 500,000 US/sat for reusable. (this isn't mentioning that a reusable Falcon 9 can support a higher launch rate)
If SpaceX wanted to launch 100 sats, they would probably use fully reusable extended fairing Falcon Heavy. Assuming that Starlink is at the limit of fairing height with a stack of 30x2, that would give you a starlink sat height of around 22-23cm. That means you could fit 2 stacks of 54 sats in an extended fairing, which gives a payload mass of 28,080kg. (Fully reusable Falcon Heavy has a LEO payload mass that could reach up to ~28,000kg.)