JR pass / tokyo metro line

Hello, we are heading to tokyo shortly and are just trying to make sure we understand how the metro passes work. We are staying at a place near Kagurazaka (on the Tozai tokyo metro line). We are planning on going to Kyoto for a visit and to mount fuji.

Based on the Japan rail pass calculator, these trips (along with to and from the airport trips) aren't worth getting a JR pass, and instead we should just get a Pasmo for the metro and just pay the fare for tokyo-kyoto. Is there any other things the JR pass might be useful for around tokyo? For instance is it a bunch faster to get around the city on the Yamanote line than just the subway?

Thank you for your time and help.

I consider a JR Pass within Tokyo to be of limited use, and I think most would agree. It's pretty difficult to actually get your money's worth over the course of a day.
The Yamanote line is not inherently faster or slower than the subways. Whether one is faster than the other depends entirely on point A and point B.