Because of the #1 complaint on the list.
The genesis of Shaky cam came (with the Bourne Supremacy in 2004?) at a time when films were featuring increasingly choreographed yet unrealistic feeling action and/or were replete with CGI filled action imagery.
It's immediate predecessors were films like The Return of the King, Pirates of the Caribbean, Terminator 3, Underworld, X2, Lara Croft 2, Charlies Angels Full Throttle, Bad Boys 2, Hulk, the League of Extraordinary Gentleman, The Matrix Reloaded and The Core. Many featuring highly obviously, or over choreographed, balletic action (popular after Crouching Tiger Hidden Dragon and John Woo), or uncanny violence, often relying on computer generated imagery. Consider scenes like the Olyphant and Ghost army in RotK, and the almost clicheed heel high kicks of Angels among many instances of action seeming silly or superficial. Shaky cam went a long way in countering both those tendencies, of action being merely appreciating fluid dance performance, or slick computer generated imagery. Master and Commander, and the last Samurai seem to have a more naturalistic bent, CGI enhanced rather than reliant, featuring mostly real sets and stunts, and live action oriented to their credit.
This isn't saying they're bad films, just they depicted action differently. The CGI often works for many, like the Return of the King (exceptions being scenes like maybe the Ghost army and the Olyphant), but gives the sense of having a polished CGI veneer. Even Kill Bills dramatic live action while both stylish and theatrical, has rather comic gore (like ridiculous amounts of squirting 'blood', yet remarkably unblood-like) and relatively farcical realism (the Heroines recovery, almost absurd number of amputations and instakills and much more). Few would likely remark many of these films are extremely gritty, very tense and realistic.
By contrast framing action with shakiness, returned gave the audience an uneasy chaotic feeling (why some didn't enjoy), promoting a tone of unpracticed, unchoreographed unpredictability, trying to create a sense of it being physically improvised (while of course being not). Visceral elements (one might say realistic) of violence lacking when contrasted with by what had by then become almost the action norm.
Of course then Shaky cam has since been overused and abused, almost as much as the style and tone it was used to counter. Without the necessary extra disciplines of doing other things like the necessary camera work, acting out violent actions and reactions (grunting, being hit etc), physical choreography and editing just as well to match, by itself it's just a cheap and easy gimmick to make things seem gritty and realistic, and is about as successful as every cheap and easy gimmicks.