note:this is my oppignion given the writers would admit other wise I would still think like I do.
I stand with what I previously stated , blood bending as fancy as the name may sound is still water bending , they're not bending the actual blood of the persone, then I might of agreed with you but the fact of the matter is , they use the moons power to be able to detect the water in the ppl's blood.
IMO freezing water into ice in seemingly tropical temperature seems more like a mastery of your element then using the moons power to detect water in someones blood .
I reckon water benders (from living in the south and north poles) had a more accessible way to learn how to controle ice , wich is why most ppl reject it at first as a mastery since a water bender that uses ice is quite common and most ppl seem to be under the impression that the mastery has to be something unknown or " exclusive " like metal and lightening bending
I know alot of ppl will disagree with me but I really belive what I said ,I'll admit blood bending is awesome , its a dangerous , almost unknown skill but it dosn't fit in the cathegorie of an element mastery , its just regular water bending , pushed to its limit
Edit: to reply to your edit
the 4 masterys are part of the elements, each mastery element is a branch of their main element , I dont understand why the avatar couldnt learn them , in his avatar state aang could even use 2 elements at the same time , when he morphed into avatar roku he melted rock into lava thus using fire and earth bending at the same time
Edit 2: and while reading your first post I was under the impression you were talking to me as if it was common knowlege that blood bending existed at the time I created this tread , roughly 2 months ago , let me assure you I'm perfectly up to date with the Avatar serie , i'm currently at episode 11 or chapter 10 part 2 if you prefer .