What is the reason it is disliked or impermissible to drink from a broken or a cracked vessel ? Also should such a vessel be discarded despite being almost intact ?
The first thing which comes in mind is that it eventually may harm the lips to drink from a broken or cracked vessel and maybe some of the liquid wull run out on one's cloths and body. This is one of the first reasons quoted in commentary's of such a hadith like in 'Awn al-m'abud beside the fact that water or whatever one is drinking may run out and drops may fall on the person who drinks (in the comment literally: on his face) and his/her clothes as one the liquid would be hard to keep in such places on a vessel without running out etc. An other reason is that some have called it the seat of satan, the commentator here explained because such places on a vessel are hard to clean correctly so drinking from their may be with the lack of the needed purity and cleanness.
Note that there's a weakness in this hadith as one of the narrators Qurrah ibn Abdirrahman قرة بن عبد الرحمن بن حيويل المصري is considered as da'if (weak) by Yahya ibn Ma'yn and munkar (rejected) al-hadith by Imam Ahmad.
Note: impermissible here has been understood as makrooh (disliked) not as haram (forbidden).
I've heard one opinion from a scholar that bacteria can grow in such places, so it may be armful. This is one of them sunnahs, where there definitive wisdom has not been stated. Another point is that Islamically, items should be in a wholesome state, for example, you should not wear torn shoes.