The main reasons is simplicity and habituation:
A prusik made from a loop is easily taught and controlled. This is a point that many experienced climber forget about often: When people start they may struggle on the basic knots. So for the first thing to learn a simplicity is more important than functionality. And the prusik is a long established and reliable knot. Safety is good too: Just check the knot before use and add a turn if more friction required.
Why do many people stick with it?
The simplicity is reason again, but the other is simply habituation: It is much easier to simply stick with what you learned, it feels "comfortable". Another important aspect is interoperability: You (almost always) climb with a partner and should control each other, so all the knots must be known to both climbers. So you have to employ the smallest common denominator of knots, which is usually the more basic knots.
Other uses are in mountaineering when on glaciers you use a prusik on the cord and hold the sling with your hand. This can then immediately be used for a preliminary anchor. For climbing I do not see any other uses.
Why not the arbory knots you showed above?
I think this is only for historical reasons: Different knots evolved in these two areas that had probably not significant enough overlap to merge. I can do a prusik without a pretied loop (you just need to secure the free end with e.g. a double fishermans). I learned this for a variation of a pulley in crevasse rescue, but it is simply more complicated: You have to do knots on both ends of the cord while in a loop you can just clip into. Here your point of cords with eyes in them comes into play: I simply never saw such a thing in climbing and as you stated I have no idea about splicing. So I guess definitely a culture thing (a friend of mine is arborist and avid climber, never saw one on him either).
Still many people I climb with do use other friction knots. Some do not carry a pre-tied loop for prusiks with the argument that it can only be used for this single purpose and is thus ineffective. They use slings instead. I often use a longer pretied loop to do a knot we call "Englaender-Prusik" (literally: Englishman's Prusik, heard of it as French Prusik too :P, correctly: autoblock, thanks Mr.Wizard) for which you simply wind the cord some times around the rope and attach both ends to a locking biner: Easier and you cannot drop the cord as one end can always stay in the biner.