If you are using city/municipal tap water, and changing the res daily (cleaning the bucket too), you probably are preventing pythium, and even don't real eye it.
Most city water sources already use chlorine and chloramines. The chlorine itself would dissipate fairly soon with air stones (less than 24 hours), but the chloramines would stick around long enough to help out.
That and having a temp lower than 70. Any higher than 69 degrees is hitting root rot territory. Not to mention lowering your dissolved oxygen levels.
Pythium isn't the only fungus/bacteria that can cause rot. There are many things to look out for, and variables that could cause root issues.
A water chiller could keep things at bay, but who really wants to fork out for a low hp chiller, especially for a small hobby grow?
Most options involve using some kind of beneficial bacteria (like hydrogaurd, etc).
Pool shock is probably the cheapest method, and what I would use if I kept having issues.
Where I grow.. in the late fall/winter/early spring.. I actually have to use aquarium heaters to warm the water up.