When boiling water, why start from cold?

Question

A question about probably the most mundane subject in cooking: boiling water.

For cooking techniques where you drop ingredients in simmering or boiling water - such as for vegetables, pasta, many rice recipes - I have often seen the recommendation that you start by putting cold water into a pot, then bring it to a boil. Why would you not start with hot water from the tap? It's going to be quicker than heating cold water, and your water heater is going to be way more energy efficient than your stove top at heating the stuff.

In particular, is there any physical or chemical process that starting from cold water encourages or prevents from happening?

(To reiterate: in the case where you add stuff to cold water and then start heating it, there clearly is a difference with starting with hot water; this question is about the case where you drop your ingredients in pure water that's already boiling.)

Answer

Some people say cold water boils faster than hot water, this is false, found here and here.

One reason might be (from the first link): "Some water heaters may introduce additional sediment into the water, giving you another reason to consider starting with cold—at least, if time is not of the essence."

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