I would guess that having loads of dead algae in your drinking water is not much better than live algae. You want to keep assorted gunk from having a chance to grow in the first place.

But certainly the water is filtered before reaching homes, considering it rests a long time in a open reservoir. So you could remove the dead algae. Still, they certainly have a "better dead" approach, wanting the reservoir to be a dead pool instead of a living ecosystem where they'd have to monitor what is growing and how dangerous it might be.

It's interesting to compare different systems. Here's one for a small part of the UK. Our tap water (from thefaucet) is vety high quality.

http://www.thameswater.co.uk/cycles/accessible/water_treatme...

The last stage of the process is to add chlorine to the water.

Just a guess, but maybe chlorine needs a good amount of time to be effective, and the transit time from reservoir to tap might not be enough

Why not use ozone to teat the water. It's a better solution that chlorine, even more effective to kill bacteria.

Why not, indeed...

Bromates are formed many different ways in municipal drinking water. The most common is the reaction of ozone and bromide.

Source: https://en.wikipedia.org/wiki/Bromate