Reasoning questions on eclipses why doesn't a solar eclipse occur in every new moon?

I know one reason is the inclination of Earth's orbital plane. But is there another?
Let me put it this way.  If the Moon's orbital plane where exactly aligned with the Earth's orbital plane (which, by the way, includes the sun, not surprisingly) then there would be a solar eclipse on Earth during each New Moon.  But, in fact, the Moon's orbital plane moves about by many degrees in a very complicated fashion.  Figuring out why this was and how the plane moves kept Isaac Newton busy for a few years.

Both the Moon and the Sun subtend about 1/2 of a degree on the sky.  The distance to the Moon also changes considerably, so its angular extent varies around this 1/2 degree. So, to get a total solar eclipse, they need to be aligned to a very high degree and the Moon needs to not be near the far edge of its distance range.