My hot water tap is supplied by a combi boiler which heats the water on-demand, supplied by the same cold water source as my cold water tap. As a result, I'm confident that the water is reasonably fresh and clean. I don't use it for brewing tea or coffee, but I'm happy to boil vegetables and rice in it. It saves a couple of minutes bringing the water to the boil.
My parents' hot tap is supplied from an insulated immersion heater tank. The same water can sit in there for days, and it may heat and cool several times in that period. It is supplied by a header cistern in the attic. Last time I looked at the header cistern, there was a crop of dead flies floating on the surface, and some unidentifiable gunge settled at the bottom. This hot water is suitable for bathing and cleaning; it's not suitable for cooking.
If you don't know the details of your plumbing, and you're not sure it's safe, don't cook with water from your hot tap.