Why wouldn't it use or support plain SMS? The satellites are emulating cell towers to be able to talk to existing modems in existing phones, and SMS is one of the most barebones things you get "for free" when you have a functioning connection before voice or data are even on the table.
The link budget, latency, and number of devices per cell/spot beam are significantly different for satellite applications and have so far required adapted protocols.
These are all not huge adaptations, and the hardware (antennas, LNAs, power amplifiers etc) of modern phones are definitely capable of it, but this entire endeavour is so much easier if you can just slightly adapt the cell phone side of things as well.
5G has made these adaptations (for both NB-IoT and "regular" 5G, i.e. NR); I'm just somewhat doubtful Starlink will be able to deliver the same for completely unmodified 4G/LTE.
