You don't need a self-chlorinator. They use tablets that are a stabilized form of chlorine. If they are used too long, too much stabilizer (CYA) builds up in the pool and if you don't run higher than normal chlorine levels as a result, then you may have algae problems. (Take a look at the Best Guess chlorine chart in my signature below.) It is no big deal to just add a little chlorine each day.

On the other hand, if you travel, you can use the chlorinator while you are away to add some chlorine to the pool.

I don't have one and don't ever plan on having one. But, some people do use them.