It might not be so much of a "wrong way" as "the best you can do" as far as a public pool goes. In a residential pool, you have a pretty regular bathing load and (hopefully) control of kids urintaing in the pool. Also you can test anytime you want and treat the water as necessary any time you want.

In a public pool, I would guess you can only treat the pool in the off hours then that has to last the whole time the pool is open regardless of how many people are in it so you end up having to overchlorinate to keep things safe.

At any rate, for that reason I wouldn't use a public pool as experience for using chlorine.

Peter