When boiling water without any other ingredients in it, why start from cold? 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.)
There have been plumbing systems in which the hot water was likely to have dissolved more [toxic|unsightly|unpleasant-tasting] material from the pipe walls or joints than the cold. In particular any system that uses lead-based solder, can leach minute{*}, but detectable amounts of lead into the drinking water, and the hot water is more efficient at this.

In this case that advice amounts to "use the clean water".

{*} Really minute. Like "Use this water all you life and not suffer any ill-effects" minute. But it can be detected, and who wants to chug down a glass of lead solution...