Why should NEVER put chlorine pucks in the skimmer? This is any easy one. When your pool filter system turns off the tabs keeps dissolving. This develops a pocket of highly acidic water.
When the system turns back on this acidic water goes straight into the filter system and within a short while can compromise the internal parts. Cartridge and DE filters can become brittle. This can wear them down faster and possibly allow dirt to return back into the pool.
Acid will also eat away at the O-rings pipes and gaskets.
You can use your chlorine tab feeder, or better yet, get a tab float. They come in all different shapes such as frogs, ask you pool technical about this.