Bleach isn't always cheaper but it is the chlorine source that adds the least amount of extra stuff to your water. There is nothing wrong with using other types of chlorine. You just have to determine what your pool needs. Cal-hypo adds calcium which is needed in a gunite pool at a level of 200-400ppm. But, if it gets too high, then you can have cloudy water issues. Trichlor pucks add CYA which is fine if your stabilizer is low. They are also very acidic which is ok if your pH runs high. But, continued use of trichlor causes a lot of people to end up with a CYA level that is way too high. Most people do not understand that high CYA requires high chlorine and when they get algae, they don't understand why. Dichlor has the same things as trichlor -- very acidic and adds CYA. All that bleach (sodium hypochlorite) adds is salt. It is also readily available. So, those are a couple of reasons why it is a good choice for many pools.

But, like you said, it is not always the cheapest nor the most convenient. Depends on individual situations.

Welcome to the Pool Forum, by the way!