WATER CHIILLER VS AIR CONDITIONER AC in sealed CO2 grow room

I have recently been reading up on sealed grow rooms with CO2 injectors or CO2 generators.

Came across an interesting cooling solution by Hydro Innovations called Ice Box.

Got me looking into water chillers. And I must say that after adding up numbers I was far less impressed with the idea after adding up the digits and estimating the cost of even a small medical marijuana grow setup using water cooling in a sealed grow room.

This in turn got me thinking of alternative and more efficient solutions to the cooling problem.

And here is what I discovered:

Water chillers for marijuana grow rooms are the most expensive component of water cooling systems. there are some claims floating around the internet that water cooling a grow room space is somehow more efficient than using conventional air conditioning systems which are far less expensive to purchase. Having given it some thought i am convinced that this is simply not so from physics point of view. I am open to criticism here and if you feel I am missing out on something in my reasoning, please do let me know by posting and commenting.

In case of using Air Conditioning to cool the air directly inside the room the compressor pumps freon (or other refrigerant) through the coils of evaporator (the cold radiator of ac unit, which does the same thing as the ice box) and the air is blown over the evaporator of ac and is cooled. Meaning the evaporator component of ac unit is functionally identical to Ice Box.

Water cooled option:
Water chiller is effectively exactly the same thing as an air conditioner, except that its evaporator coils (through which exactly the same refrigerant is pumped by the same compressor) cools water it is submerged into, instead of directly cooling the air like in the air conditioner. And then there is another circuit, which moves this chilled water through another evaporator coil (aka in hydroponic water cooling context as "Ice Box"), which in turn cools the air, thus doing what evaporator coil of the same water cooler could have done just as well (or more effectively) if it had this air blown though it directly.

Water chiller setup involves a redundant circuit of water circulating through another evaporator coil. This adds another coil, lots of extra tubing and an extra water pump.
Overall, I would imagine, that the thermodynamic efficiency of water chiller and ice box is probably very close to that of an AC unit. But it is redundant and involves many unnecessary components (therefore: more things to break down).