In sci-fi and fantasy artwork, I often see a city built on top of or incorporating waterfalls:

James Gurney's Dinotopia (above) is an egregious example with "waterfall towers". When the city is underground, there's often a central waterfall pouring into a lake. And in the film Logan's Run (below) they escape the city through a postmodern water sculpture park – it's purpose isn't explained.

Is there a utilitarian excuse for artificial waterfalls in a (mostly) realistic fantasy or sci-fi setting?

I'm looking for plausible infrastructure, sanitation, irrigation, or atmospheric purpose that would justify the expense and maintenance of channeling artificial waterways through a city, or deliberately building a megastructure city on top of natural water channels and cliffs.

A watermill in every home does not sound like plausible infrastructure – even in a medieval watermill-punk world. I can't imagine that thousands of localized water turbines (even Tesla turbines) would be better than a large centralized hydroelectric powerplant. (Maybe I am wrong?)

How can I justify a City of Waterfalls trope to serve a plausible utilitarian purpose?

As suggested by the two photos, the waterfalls don't need to be impressively large or in any particular configuration, just open-air and scattered throughout the structures. I want the form to follow function – whatever that is. My setting is sci-fi/fantasy (no magic, not Earth, all human) with refugees living around repurposed heavy industry, so my "waterfalls" need to serve a utilitarian function (at one time if not currently).

I am specifically not looking for aesthetics or "because they can" reasons, such as the waterfall skyscraper in China, rather a utilitarian or infrastructure purpose.

Still water is heaven for proliferating algae and bacteria.

A large city with large bodies of still water is a recipe for plague spreading. Having water on the move keeps the water clean and, as a consequence, the city healtier.

Also, waterfalls help enriching the water with oxygen, helping bacteria to decompose organic matter suspended in it, again improving cleanliness.

Energy storage.

You use a form of energy generation with unreliable or periodic output. As a form of energy storage you pump water up into a nice big reservoir when you have surplus, then power turbines by letting the water spill back down to a lower reservoir to create a more steady power supply.

It might be more efficient in an enclosed system of pipes, but for aesthetic reasons and public morale it’s much nicer to have exposed waterfalls in public spaces.

It’s pretty simple, pretty reliable and pretty.

Waterfall is power

In Shannara Chronicles castle of Humans was built on what looks like hydroelectric dam:

Both having electricity (or other kind of energy if it's fantasy) and being able to dry or flood large terrain is pretty utilitary, and nothing shows it off better and is foolproof more than simple waterfall - it keeps maximum level of water in reservoir without any moving parts that could break.

Graduation towers

If you have a salt mine nearby, waterfall can be used to increase salt in solution, an important step in salt purification. Sure, most common design is based on wooden sticks, but regular waterfall requires far less maintenance.

There are several purposes which you can fulfill with a structure of channels and waterfalls.
On the one hand, channels within your city provide a fast lane means of transportation in any age of human technology. As L.Dutch pointed out, keeping the water moving instead of standing still keeps bacteria and algae from developing into serious health problems for your citizens. They can also provide either a source of fresh water or a sanitation possibility (more plausible in a low tech setting) for your citizens. Definitely, if have water channels and even more so, if you have water falls, you are provided with a natural way of micro-climate regulation. Cities tends to heat up in summer time/during heat periods, which water can compensate providing a cooling effect and keep the air from becoming too dry to make infections of the respiratory system more likely. In addition, the aesthetic effect of water channels and park lanes or avenues alongside it should not be underestimated - it keeps your citizens happy alongside more efficient infrastructural uses. The platforms above water falls can also make attractions for the city's more advantaged citizens/nobility or possibly every citizen and demonstrates the power of their ruler to be able to build such an amazing structure.
In addition, these large waterfall structure can actually have the turbines of your city-wide power plants at their bottoms without limiting the effect of any of the advantages listed above.

refugees living around repurposed heavy industry, so my "waterfalls"
need to serve a utilitarian function (at one time if not currently).

Vital minerals were found under a large natural waterfall (Niagara etc.) In order to mine them, a way of diverting the water away was invented that didn't require changing the course of the whole river. That was impossible for large-scale geographical/geological reasons.

The old civilisation simply built chutes outwards from the top of the existing falls. Eventually the outward aspect of the mine became huge and more and extended chutes were added at different levels. People who lived at the mine workings had their own personal chute to keep their house or front door dry. This all proliferated in a haphazard and ad hoc way.

Low-tech climate control: the waterfalls fill the air with spray, which evaporates off and cools the populace.

The Romans used to achieve a similar effect with fountains.