Whilst ligatures may have lost much of their original function in modern print, that is to say printing from digital files, they were (and still are) an essential part of traditional letterpress printing - that is, printing from metal type. Original metal type is cast so that each letterform sits on its own block, or 'body'. When certain combinations of letters are used, (for example 'fi' or 'fl') it is physically impossible to reduce the spacing, or 'kerning', enough so that these combinations appear to have the same kerning as the rest of the type. This is due to the width of the block, or body of the type, that the letterform sits on. If you were to scan your eyes over something letterpress printed from metal type where ligatures had not been used, the spaces between combinations such as 'fi' and 'fl' would appear too large. So the only way to achieve kerning that is visually correct, is to cast these letter combinations into one single block, known as a ligature. This allows the two letterforms to invade or overhang each other's space slightly, since they sit on the same body, and results in visually correct kerning.
I would conclude that traditionally, in letterpress printing, some ligatures such as the 'fi' and 'fl' combinations served the purpose of ensuring visually correct kerning as described above. You would, of course, still be able to read and make sense of text that had been typeset without using ligatures, but it wouldn't be as aesthetically pleasing, and would appear 'gappy'. Fast-forward several centuries to modern type design and the same principals apply. Many faces are still designed to include common ligatures such as the 'fi' and 'fl' combinations, because it simply looks better if these combinations are allowed to encroach on each others' space, when using default kerning. In contrast, you can see from the images at the top of this post that the 'ct' and 'st' combinations don't really need to encroach on each others' space. You could draw a vertical line cleanly between the 'c' and the 't', and likewise the 's' and the 't'. So I think these particular combinations are more likely to be decorative as opposed to functional in terms of visually correct kerning - they wouldn't have needed to have been produced as ligatures. But their presence in type may well date back to their historical use in handwriting, when perhaps joining those combinations of letters together allowed for faster writing, or represented a contraction eg. 'saint' became 'st'. Bearing in mind the fact that before the invention of letterpress printing it took around 3 years to produce a single hand-written copy of the Bible, scribes were undoubtedly looking for short-cuts to speed up that process!
So should you use standard ligatures as default in desktop publishing? I would say yes, because they have been designed to ensure that type reads smoothly without looking 'gappy' when set using default kerning (spacing between letterforms). Discretionary ligatures are more likely to include more decorative letter pairings such as the 'st' and 'ct' pairings at the top of this post. As a graphic designer I might use them as an interesting visual element, for example in a headline on a magazine page where I wanted to make a feature of the type. But I probably wouldn't use them for the body copy on that same page, as, over a long read they could be quite distracting.
Hope that helps answer your question.