Michael:   You asked what the intention was when writing an action scene...action scenes move the story along, usually increasing the pace.  In some genres, intense, almost constant action is expected by readers; in others, low-intensity (nonviolent) is expected.   So the genre (which gives you the reader expectation for that kind of book), the position in the story, and the overall plot arc and character determine the intention...my intention is always to glue the reader to the book.  

I agree that action doesn't always mean the ninja team crashing into the room, or car chases with explosions (that staple of action TV and movies).   An action scene is a scene whose plot relevance should be immediately obvious (something's happening, and it's important in some way) and in which the character is strongly motivated to do whatever action it is.  Find something, start something, stop something., etc.    Fashion also comes into it--there was a time when thrillers started more slowly than they do now, but visual media have conditioned readers to expect something to happen immediately.   Thrillers are nearly always one-volume stories;  epic fantasy, which is often multi-volume (to give room for the scope of the story, the cast of characters, etc.)  can start a little more slowly (not slowly, for modern readers) because it has plenty of room for action later. 

Good action scenes  have their own arc, and are integrated into the larger overall story arc.  The scene arc rises higher and has steeper "slopes" than a non-action scene.  Action scenes are great for revealing character while moving the story along (characters and readers both react strongly to moments with perceived higher risk...risk of anything.)   It helps to have established the character first (even if this scene is going to reveal something new about the character) so the reader isn't trying to juggle too much at once.  I agree that the scene should--while the action is going on--keep a focus on the character's motivations and reactions to the action.   This lets the reader experience the action rather than just watch it.  But the arc also matters...from the character's realization that he/she must do something through the doing of it to the result (good or bad)  that ends the scene arc and sets up the next scene.

In an action-heavy book, it's important to vary the kind of action scene--if it's car chases from start to finish, that's going to wear out after a short time except for car-chase enthusiasts.   The reader shouldn't ever become jaded with one kind of action scene, or one level of intensity, or one motivation getting the protagonist into a situation.   There may be a "big" motivation (revenge for the killing of a family member) but along the way the protagonist will have others--he's hungry, tired, confused, bored, annoyed with people for something not related to his big motivation.   The minor motivations lead to action scenes that may in fact connect with the big one (while stopping at a diner because he hasn't eaten since the day before, he overhears something he thinks has to do with his quest, but asking questions leads to being recognized as the grieving father who was on TV last year asking about his missing wife/daughter/son.)   Variations in intensity, spacing, and type of action make a book more interesting and less predictable.