"Lime water" technique -- why use an excess of cal?
The supersaturation of cal seems to be the common instruction in most online sources, but no reason is given.  The best reason seems to come from chemistry texts, which note:

Ca(OH)2 is only slightly soluble in water (0.16g Ca(OH)2/100g water at 20°C) forming a basic solution called lime water. The solubility decreases with increasing temperature. The suspension of calcium hydroxide particles in water is called milk of lime.

According to Cook's Illustrated, you are trying to get as much lime into the water as you can, since your target is an extremely alkaline (pH 12.4) solution.  So .. if it's hard to dissolve Ca(OH)2, and you're going for maximum saturation, dump a whole bunch in and pour off the solution.