I don't recommend reefers trying to handle Calcium oxide as it is an irritant to the respiratory tract and it is higly exothermic when it comes into contact with water.
A much safer alternative is Calcium hydroxide to be mixed with water a.k.a. kalkwasser.
The idea to precipitate phoshates out as calcium phosphate is a good concept but the resultant solution will need to be saturated with calcium ions. What is formed is essentially no different from kalkwasser or calcium hydroxide solution (same thing is formed if calcium oxide is used). This solution is too alkaline to be used as water for mixing. Any salt mix added to it will result in massive precipitation of many metal ions resulting in an unusable slurry at the bottom i.e. waste time, waste money.
By bubbling air through kalkwasser or calcium hydroxide solution, you are allowing carbon dioxide to react with water and excess calcium to form insoluble calcium carbonate. This can reduce the amount of calcium in the water and reduce the pH. The mixture will then need to be tested to ensure calcium levels have dropped to a low level before filtering to obtain the liquid.
In my opinion, although this method of phosphate removal in freshwater is conceptually and chemically correct but the procedure is tedious and difficult to ensure the suitability of end product for use with salt mixes without numerous testing. Filtering huge amounts of liquid to remove precipitates is not feasible in the average home without a vacuum pump and proper apparatus.
If the reefer is convinced that the phosphate level in the tapwater is high enough to be of concern to the tank, then buying distilled water or installing an RO/DI unit will be the best and economical way on the long run.