They disallow consecutive days off so that no employees are going to have a situation where they feel comfortable leaving town on a trip, so that they will always be around the store. They screw with employee hours so that employees are unable to hold a comparable second job.
Another problem is companies that intentionally book non-consecutive days off for their workers are also going to do everything they can to discourage workers from taking time off when they want to.
I also assumed as a part-time worker I would be at the will of the employer even more; I myself have never done part-time work like that
You lost me there. When I worked shit retail jobs I was actually laughed at when I tried to schedule 3 days off a few months in advance.
Hell my first job was at a place where they would not tell you your schedule over the phone or over the internet and they would change your schedule the night before they wanted you there. Unless you were willing to drive to the store every day, even on your day off, you would never know about new shifts you had assigned and would subsequently be a no call no show.
The managers used this so they always had a safe reason to fire someone. When you did something they didn't like but was protected by store policy or legality, they would just fire you next time you missed one of these sudden shift changes.
Their transportation is usually unreliable because they can't afford to purchase a new car or maintain the vehicle.