Binding composite component's input field to variables?

Is it possible? It is looking like composite components are more trouble than they are worth. Any time saved on replication is wasted 100x on trying to make them behave.

Ok, finally, I was able to bind an internal field to a page variable. Could you, guys, make it any more convoluted? And in the end, this complexity provides neither more protection, nor ease of use. There is literally no reason to do this.