What kind of clown show operation runs out of chicken on a consistent basis during the dinner hour? One that I won't be going to anymore.
I say the following with the caveat that my restaurant career back in the 70's to early 90's was never in fast food.
I'm assuming nowadays, a restaurant is going to have some sort of system in place where they have an anticipated amount of product they're going to need to have ready to go at certain times of the day. Called it a PAR level if my memory is good. This assumes they (Popeye's) have a pretty good idea when they're going to need a shitload of chicken to sell (and when not to).
For example, they'd need X amount of chicken ready to go at 11am to 1pm, 4pm, 5pm, 6pm, etc. This also assumes that they are staffed with competent management, employees, etc...to adjust if demand is higher or lower than those PAR levels. But what you really want to avoid if at all possible is to have too much made at any particular time because once food is cooked, the proverbial clock is ticking as to how long you can keep it in good enough shape quality-wise to sell.
You might have simply gotten there at a time where (just before you got there) higher demand than usual drained what they had on hand, and the powers that be were slow to react.
I know that sounds like Captain Obvious type stuff - but it is sort of a dance a place that sells for example fried chicken (a type of food you just can't cook an entire evening rush's worth of chicken at 4pm and never drop another basket the rest of the night) have to be really good at to get it right, always.
Think of a drive-thru chicken place versus a mostly buffet place like Pizza Ranch. At a PR, all you have to do is see how many people are in your dining room/buffet and check out the register line to guesstimate when the next basket drop needs to occur. The "ranch hand" watching the buffet goes out, sees the buffet pan half full yet the dining room is rocking...boom, drop 2 more baskets.
At a Popeye's though...not as easy to do that. And given your average basket of chicken probably takes anywhere from 10 to 15 minutes to fry...yeah, 15 minutes (or even 20 to get it actually into your hands) - not really surprising.
Not apologizing for them - but to me, fried chicken is probably something that is more prone to things like this more than most drive-thru foods.