TWOK is really the first part of a trilogy. Taken as a whole, the TWOK/TSFS/TVH trilogy is bolder, grander, more dramatic, and ultimately more satisfying than most individual episodes of TOS. Looking at them that way, we see a symphony that overshadows the faults in each of the individual films.
Long story short there, the TOS films managed to transcend the limitations of TOS on TV. They took us places far beyond where we'd been before. They freakin' killed off one of the most popular characters in TV history, destroyed the Enterprise, and then brought it all back by the end of TVH.
Did the TNG films ever manage to do something similar? Nope, not even close.
Dude, you nailed it. I think another reason why TOS movies -- particularly the three you mentioned as a trilogy -- feel like a larger story (than TV) is because so much time had passed before they actually made a TOS movie. Effects improved, styles changed, and the passage of time also provided nostalgia for the audience. Lots of interesting thoughts in this thread.