Serious question, as daft as it might sound - do they have to chlorinate the water to stop stuff growing in it? I'd expect it'd be about "swimming pool" warm so just great for all sorts of manky algae growing.
The water is borated and heavily purified. You don’t want stuff growing inside, but at the same time you don’t want to have chlorinated water slowly corroding the metal components.
On the picture, the fuel rods are indeed protected by a huge quantity of water above them. But what happens below them ? They seem to be in direct contact with the ground...
Chlorinating the water would have adverse effects on material strength and longevity. Even irradiated and heated to 50c, I’ll bet there’s some extremophile bacteria in there somewhere.