Ca(OH)2 is a strong base, but its low solubility limits how high you can go with pH. If ammonia is a base strong enough, it shouldn't matter.
Low solubility of Ca(OH)2 can have a negative impact on yield, making the idea not economically viable.
Note that CaCl2 is highly soluble. Perhaps not as soluble (in terms of molarity of the saturated solution) as NaCl, still, not something that you would classify as low solubility.