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”.
Non-competes make it harder to find a new job. Employers want it to be hard to find a new job, since that means it’s hard to leave your current job even if the pay/hours/whatever is poor.