This one has been going around my head for a few years. I can’t see why it wouldn’t be a good idea.
In most houses (except mine), each cold water tap is at mains pressure. When you turn the tap on to brush your teeth upstairs, you only open the tap a little really, you want just enough pressure to wash the toothpaste or soap away.
Why not attach a small impeller to each tap? When you turn the tap on, the water flow would generate a small amount of electricity. This won’t generate much but will make use of the energy used to pressurize the mains water rather than it just swirling around the basin.