I did this for years and didn't have any problems, with a heater. The pool original came with a chlorine tower but I could never get it to work right so I just through a tablet in every 3rd day and ran the pump for 8 hours. I live in Fort Worth, hot summers.
I have recently gone to a floater, after reading all of this, but I have serious doubts about some of what is being said. The tower, the floater...etc, are all made of pcb tubing and plastic and they don't get brittle and break as many have claimed here. The floaters deterioration is usually from sunlight and weather. My basket is the original skimmer basket I have had for 10 years. I have no stains (not in the pool anyway). But, fear has lead me to discontinue this practice for now. It was a lot easier to just throw a tablet in on the 3rd day than chasing down a floater.
I'm not sure if it was this board but someone compared it to driving your car at 90mph and how you "are taking a chance" by putting cholorine talbets into a skimmer. . There is no comparison there. Chemicals breaking down pcb aren't by chance (if it happens) and the car doing 90mph depends a lot on the driver, the car, the road and conditions. Some people are as comfortable in a car doing 90 as others are at 50.
Anyway, thanks for the insite.