My sister worked at Subway and had to sign a noncompete that she wouldn’t work at another sandwich shop for three years. Are they really afraid she’s going to steal their secrets of placing meat on bread?
The more cynical will certainly assume malice, that the company did this to keep you from leaving. It particularly at the time it was not hard at all to find new fast food workers, and I am a firm believer in Hanlon’s Razor and never assume malice when incompetence will do. I genuinely think the explanation could just be Subway’s lawyers were like “everyone else is doing noncompetes”.
I worked in Massachusetts (which allows non-competes) early on in my career, and at one point took my contract to a lawyer. He was like "This was written by a California law firm. It has clauses that are specific to California law." (One of them was that it specifically did not have a non-compete, carved out in the contract.)