This isn’t correct. Even when someone who has lost weight hits caloric balance they stay hungry. Fat cells produce hunger signals when it’s at lower than it’s previous stored energy levels.
It takes several years for fat cells to adapt to the new normal and not try to reach their previous levels.
In addition to what you said fiber is an important part of poop. An not just as stuff to push through the tract.
A important function of the liver is body detox. One way the liver does that is to package chemicals so they bind to fiber and get flushed out of the system. Lack of fiber can cause those chemicals to stick around and cause more problems.