I'm going to note before I write what I have to say and post the image, that I am not suggesting that function sets will combine in the exact way that I have listed in the image. The point I'm trying to make is that people may have an overarching type, but it doesn't really sum up the person well.
Every single interaction in life codes us in a specific way. Even though we may identify with one type, it doesn't mean that we are purely that one type. We are a combination an extreme range of interactions that combine together that gives us an overall personality, so attempting to completely identify with an idealist set(a personality type) will always fail.