Why doesn't bagged ice you buy at publix stick together. The ice cubes
Stay separated even after weeks in the freezer even after the defrost cycle . Not like my ice maker
Where the cubes stick together into a block. I do not have a water softener
Or water filter attached to the water line. Do you think that may make a difference

Oh, most definitely. Plus when they make the cubes in the first place, I am quite sure that the ice is frozen at a lower temp as well which stabilizes the water content. The water is much different than what you get out of your home faucet as well. Being in Florida there are all sorts of "other" things in the water like a lot of tannen material which makes it brownish or sulphur which gives it a smell. If you had a charcoal filter in your home and made ice cubes yours might not stick together if the water was "clean" enough.

That's why store bought ice cubes cost more.

Just like the ice manufacturing plant down the way has a sign "Made from a secret family recipie".

Odd: make crystal clear ice! (http://www.instructables.com/id/make-crystal-clear-ice!/)

Your freezer also may have a defrosting cycle, so that it gets warmer and maybe your ice is melting just a tiny bit and then freezing together.