The faucet seems a bit drastic. I got a 1L (about 32oz?) spray bottle of Isopropyl alcohol, and use a small spray amount onto a microfiber cloth to clean iPhone and iPad screens. It’s really cheap and seems to last a long time, as only a small amount is needed.

It will degrade the oleophobic coating of the screens quicker, but I figured that would wear off over time anyway. So far it’s been really effective at wiping off all greasy fingermarks in seconds. I like the window/glass type microfiber cloth for this.