If the pump
runs continuously, the chemistry does not get bad in the skimmer or in the system.
For example, if you have 7 tabs in the skimmer and it takes 3 days for the tabs to dissolve, this is the chemistry effect downstream at a flow rate of 30 GPM .
If the pump stops, the chemistry gets bad fast.
If there is
no heater and the pump
does not stop, then I might use tabs in a skimmer, but it is a risk that you have to understand.
The problem with a floater is that trichlor dust or particles/pieces can fall on the floor from the feeder and cause damage for cheaper tabs.
If the TA is good, the pH will stay in range.
Before using trichlor, add the equivalent amount of weight in baking soda (X 1.15) to the pool to offset the expected pH and TA drop.
For 7 trichlor tabs (49 oz.), add (49 x 1.15 oz = 56 oz) = 3.5 lbs baking soda to the water to offset the acidity.