Expressions starting "as.." tend to refer to the current state or condition of a person or thing.
I take your three examples in turn:
"He's very good looking as he is" means he is already very good looking and does not need cosmetic surgery, a new hairstyle, etc, whether to impress you or for some other reason (e.g. vanity).
If things are good as they are, they are good in their current condition or state. It is implied that no improvement is necessary and to attempt any may be misguided. To say "things are good as is" would be extremely informal, bordering on an error.
We use "as it is" as you have shown when things are already bad and we don't want them to get worse. We have four slices of bread left as it is (we only have a little bread and excessive consumption will make the situation worse). My boss said "I cannot give you leave tomorrow because we are short of staff. Three people are sick as it is".
You can omit 'it' from none of your examples. "As is" is a casual, informal, idiomatic phrase meaning "without alteration or further work done; in its current state", sometimes used with a hyphen: as-is. Your house is nearly ready: you can wait a week for the painting to be completed, or you can accept it as-is.