Umpires are evaluated over time, and their assignments, particularly postseason assignments, are determined in part by those evaluations. See for example Grantland's piece on this:
“The main component in the selection of Umpires for Postseason assignments is performance during the season,” Teevan wrote. “We factor in results from the Zone Evaluation system for their plate assignments, accuracy on their calls and rulings, and observations of their work by our Supervisory staff. In addition, there is consideration given to an Umpire’s experience level (overall seniority and previous Postseasons), his proficiency at handling situations, health and time missed during the season, and a number of other administrative factors.”
Now, they don't seem to actually consistently pick the best ball/strike callers, as the rest of that article goes on to say... some of that is union rules I imagine, some is wanting older more experienced umpires (who may not be quite as good at balls/strikes due to eyesight issues or whatever). There's nothing to say their evaluations don't contribute, but they don't seem to contribute enough to make a statistically significant difference in the final outcome.
Were an umpire to be a true bad actor, and actively try to harm the game, MLB could take action through their collective bargaining agreement, but that's not happened in the MLB. See, however, the NBA and Tim Donaghy for an example of how that might play out.
The other major issue here to consider is that the rule specifies judgement calls. Meaning, any call that is considered up to the umpire's judgement, and not a clearly factual in-or-out, is not reviewable - but anything that is based on some factual detail (such as, did the runner slide into the bag, did the ball hit the player, etc.) is reviewable, and the umpire has no say in the result - it's entirely up to the folks in New York at MLB HQ to make the decision, the umpire just relays the result.
Now, of course, why is balls/strikes considered a judgement call... that's up to MLB to define, but it is how they chose to define it.