Succesful examples: Lost Planet, Devil May Cry, ZOE2, Contra.
DMC is very much varied in the overall pace of the game.. You spend alot more time working your way through puzzles (of the "take this key to here, take that object to there" kind rather than the "push this box" kind of puzzles we all kno and love from the days of yesteryear..) than you actually do fighting.. The pull is that fighting is a means to break up the puzzling and vice versa..
Also with various strategies required for combating the various enemies, added to that the amazing mini-boss & boss battles, make the overall flow of the game a joy to behold..
The same can be said for ZOE 1 & 2, Ninja Gaiden, God of War, Primal and alot of action games out there..
Maybe HT won't have "puzzles" in the traditional sense but I would be hard pressed to imagine a game whereby the "only" element of gameplay was the fight mechanics.. In my personal oppinion there's alot which can be done to mix up a "pure" action game in terms of diversifying the fight mechanics; whether it be having a vast number of interesting and different enemies to fight, having different fighting styles and weapons at your disposal, having different classes of attacks ranging from standard moves to supers (a la street fighter), having a depth and breadth of combo, attacks and counters to play with, having multi-tiered battles ranging from 1-on-1, 1-on-a-few to 1-on-a-thousand..
But unless there's something more.. something to give point and purpose to interactivity outside the fighting, the whole system may not just feel right..
Any action games developer will tell you that no game can have the player fighting "all the time".. Even in Dynasty warriors the player gets some relief during combat prep where he can attend to character development, configure his forces and do other things to break up the action a bit..
If you have a game driven by a strong narrative then there must be parts of the game where the character is expected to perform so task which doesn't involve violence and without any non-fight mechanics the game forces such events to be either scripted or represented to the player in a cut-scene.. This would hurt the overall experience in my oppinion as it would push the player to feel like he is permanently on the rails, unable to take the helm of the main character until the game has finished working its way through the narrative and when another battle is ready to wage..
I don't think either NT or there publisher Sony would allow the game to follow such a path to be fair..
(I disagree with Crayon on MGS and FFX being Shallow and repetitve experiences but that's another debate for another time..)