Okay, so I've put some thought into this, and here's what I think...
Bochy and Sabean are completely flummoxed by Belt's plate approach, to the point that it either confuses or scares them, like Sabean's famous quote about "the lunatic fringe." The Giants brass simply can't comprehend the concept of anybody but a leadoff man (who MUST be your fastest baserunner, of course) or a pitcher looking to draw walks on purpose.
It boggles their minds.
Grant referred to his Jr. High baseballing career in his excellent article about Will Clark that was featured on Deadspin. He, like me, was a kid who looked to draw walks, and kids who do this in Little League are generally though of as poor hitters who are basically hoping not to embarrass themselves in front of their friends and family. This stereotype is pervasive throughout the baseball world, at all levels. As the old saying goes about Caribbean prospects, "You don't walk off the island."
Certainly, there have been lots and lots of power hitters in baseball history who've drawn a shit ton of walks. Babe Ruth and Barry Bonds to name two. However, for all the walks they drew, I doubt they ever went up there looking to walk. Even with Bonds, who was surrounded by absolute crap late in his Giants career and expected to walk most every plate appearance, I strongly doubt he ever thought to himself, "Man, I hope I can work a walk out of this guy." Bonds and Ruth settled for walks, they didn't look for them.
This isn't my way of defending Bochy, Sabean or even Henry Schulman (who I've been told by many people in the know is a certifiable dick). I fully understand that Belt is a better player than Hector Sanchez, and I for one would like to see Belt play more and Sanchez less if for no other reason than it's getting pretty painful watching Sanchez "catch."
However, it certainly looks to my admittedly untrained eye that Belt's mentality is anathema to Bochy, Sabes, and even guys like "Bam Bam" Muellens and Will Clark. He looks to me like a guy whose main objective is to draw walks, and if he has to swing, he will. It's one thing if he was a centerfielder atop the order who's gonna steal 60 bags, but for him to play a power, run-producing position and have that approach is simply unfathomable for the Giants, especially when they've got Crawford and the pitcher behind him in the order. Belt would fit in fine in lineups with the Yankees or Red Sox, because everyone there are on-base machines with power and there are no weak spots, but with the Giants sixth and seventh in the order aren't spots where you can simply hope to draw a walk with two outs and leave matters to the guy behind you. National League baseball doesn't really work that way. Maybe he'd be a better fit in the AL.
One solution I've seen raised a lot is for Belt to simply be moved up to second in the lineup, but I don't think this is a practical idea. Not only would the concept of a first baseman hitting second make Bochy's pumpkin-head explode, but can you imagine the first time Belt takes a called strike three after the leadoff man hit a double or stole a base to get to second? Your second hitter has to be a contact guy who can, at minimum, get that runner over. He can't be taking called strike threes.
Really, I think that's the biggest thing. Grant and others have pointed out that Belt swings and misses at bad pitches plenty, so it's not like the dude never swings. But I think it drives the team's brass absolutely batty all the good pitches he doesn't swing at, particularly with two strikes. We all know a double play is worse than a strikeout looking when you've got a man on base, but I think the latter pisses off managers far more than the former. A double play is what happens with BABIP, it just comes with the territory (and I think most managers instinctively understand BABIP on some level, even if they've never heard of the stat). A strike out looking is just this pathetic, weak, impotent failure that embarrasses everybody, like, "Why are we even paying you if you won't swing at good pitches with two strikes?" I imagine managers looked at called third strikes the way football coaches would regard their fullback who didn't pick up a blitzing linebacker.
It's certainly not helping Belt, for all his supposed strike zone discipline, that he's done so little with it. You'd think if he was so choosy, waiting for just the right pitch at just the right location, that he'd be crushing the ball and putting up some really impressive slugging numbers. Instead, he's slugging a tick below Nate Schierholtz. No, Belt's not an empty singles hitter like Sanchez, but he's not exactly making pitchers pay dearly for location mistakes either. Guys like Cabrera, Posey and Sandoval absolutely murder strikes. Belt isn't doing that.
Again, I'm not saying I'd play Sanchez over him, because I wouldn't, so please don't misconstrue that. I'm just saying that I don't see as much value in a first baseman you can only bat 6th or 7th because he doesn't have typical first baseman pop and hasn't shown much willingness or ability to expand his zone and produce when the situation (men on base, one or two outs, crap behind him) calls for it, as some of you do.
I think the best solution would be to bat him leadoff, but good luck with that happening. The most practical one is to trade him to the AL, where he'd be another OBP cog in the those relentless lineups. As a Giants fan, my hopes for him are the same as my hopes for every guy on the team: Please learn to swing at the good pitches and lay off the bad ones. I'm used to being disappointed on half that score, and it's no different with Belt, even if though it's totally different.