Using SMS as the control protocol seems like a bad idea. You are generating evidence with each command sent that may or may not be stored practically forever by the telcos.
Wouldn't someone using this sort of thing also buy a cheap burner phone and throw-away sim card? They're easy to buy with cash and you don't need to register them or anything to use them. Supermarkets in the UK even sell sims with credit already loaded onto them.
Some duckduckgo-ing suggests it's possible, e.g. someone wrote just go to Tesco to get one and there are no ID checks (but this was written 6 years ago). In any case, just like teenagers buying booze, it's probably not that hard to pay someone off the street to buy one for you.