The inconsistency that sometimes bothers me is why is magic really so damned, well...useless...at least in our modern sense, if it rules these people's worlds?
It seems to me you're making an unjustified assumption that magic in fact
does rule their worlds. In some fantasy perhaps, but your particular example below is notable for it's almost complete absence of magic.
Consider. In GoT or SoIaF, at least if you go by the descriptions I see here and the TV trailers, a fairly well trained and equipped brigade of 18thc British regulars could handily rout the entire Armies of Martin's world. They might need a battery of Bofors guns to bring down the Dragons but one would do the trick nicely.
I recommend reading a book before attempting to comment on it. I don't know where to begin with the above statement, but I'll merely point out that Martin's world is
medieval, and indeed, a small force of 18th Century soldiers probably would do quite well against a medieval army (I think you grossly overestimate the 18th Century army's effectiveness, but never mind). The same would be true of any significantly disparate battle between forces of one era, and forces of several centuries later in history.
I don't so much see this as a weakness, however, but rather as a pretty obvious dictate of historical accuracy and authenticity.
And the real problem is that if their wizards could simply snap their fingers and stop their enemie's hearts from beating....well that seems like even modern day soldiers would find that hard to beat.
What "wizards"? There are no "wizards" in Martin's world. Seriously. Read a book, then comment on it.
So why doesn't their magic work like that? Just asking.
Just throwing this out there, but perhaps because the writer didn't want it to work like that?
Your question is meaningless. Let me illustrate;
"Why didn't JK Rowlings make it so Harry Potter could kill people just by thinking about them?"
"Why didn't Homer make it that Achilles could come back from the dead?"
"Why didn't Bram Stoker make it so vampires were immune to sunlight?"