Why use cold tap water? Wouldn hot tap water boil faster?
Household water heaters heat water for washing, not for drinking. Water out of the hot tap generally has health-threatening levels of heavy metals (such as lead), as well as an off taste. You should consider this water unfit for human consumption. Incidentally, if you live in the United States in a house whose plumbing system was constructed between the 1930s and the late 1970s, it’s a good idea to let the cold tap run at full for about a minute before using it. This will help flush out heavy metals that may have collected in the water as it sat in the plumbing system. This goes for all tap water consumption, of course, not just for tea. Some tea drinkers start with filtered water, particularly in areas with unpleasant or unhealthy tap water. Although this can improve the quality of the final product, some filtration systems have an annoying disadvantage.