Discretionary ligatures are non-standard ligatures such as:

st and ct in Atlantica LF font

Are they purely visual or is there any other reasoning to back it up? Psychological? Letter-press related? (Did they even exist in times of letterpress printing?)

Related article on Upper & Lower Case Magazine say these are "… more decorative in nature than standard ligature[s] …" But is that all?

Personally, I find them a bit distracting, especially if they're used in long body types. Also it's hard to imagine they would have any practical value in handwriting — at least I draw the letters from top to bottom, and extra ties between letters would disrupt the flow.