The immediate practical advantage of this idea would be to lessen the effects of overpopulation by expanding the available living space many times over. Such settlements or cities could be powered by geothermal vents, or tidal energy, nuclear plants, or deep sea oil deposits.
The main obstacle to such a plan is the enormous cost of building material and overcoming the technical problems such as high water pressure and food sources.
In practice there are in existence a few shallow water facilities that serve as novelty hotels or research stations. Also, houseboats could be considered a trivial example of such.