SpaceX has a 90% market share.
The other reason they're not a monopoly is that they may do 90% of total launches, but most are for themselves to support starlink (another "nonopoly" with no competitors). They have 60% of the US government launch contracts, a small percentage of ESA when Ariane is flaky, amd of course 0% of China and Russia.
Start with "Titan" by Chernow.
SO was basically convicted of "making too much money", and the government failed to convict SO of a monopoly.