I don't think the mechanics of a system would be impossibly difficult for the NBA, but I think the substance of the system would be terribly unsatisfying to fans. First of all, as in football, I don't think that the league would (or should) permit reviews of purely discretionary calls -- in the NFL, there is no review of whether a defensive player interfered with an offensive receiver and there is no review of whether an offensive player held a defensive player. The officials call what they see and if they're objectively wrong in the moment, the recourse is not reversal of that discretionary call on the field, in that moment, but is instead a disciplinary action by the league.
I think the same would be true in the NBA, because so much of NBA officiating is subjective and discretionary. I could see that a challenge system might work to overturn an official's ruling of a block because the defensive player was in the restricted area, if the replay showed conclusively that the player was not in the restricted area, but then again, would the review also encompass whether the defender was moving or whether the offensive player accepted the ball below the hash marks? If so, what if the replay showed that the offensive player travelled, but that on the far side of the lane, a defensive player held another offensive player -- then what? Do you negate the block because of the travel but negate the travel because of an uncalled foul? I realize that from an aspirational standpoint, that might be exactly what some would want, but from a practical standpoint, I think the potential for funny business would actually increase.
I think the other impractical aspect to this is that you could, for the most part, only review affirmative calls and not no-calls, which are frequently as problematic as the calls themselves. Suppose that Pop is convinced that Duncan got mauled without a call and wants to challenge that decision, but subsequent to the supposed mauling, Kobe led a fast break for a dunk only to have Manu throw some crazy length-of-the-court pass to Timmy for a dunk and then have Parker steal the ensuing inbounds pass and get a layup and then have Richard Jefferson called for a bump on the defensive end. At that point, Pop's challenge is honored -- what then? Suppose that the officials had the power to rule that there was a foul on the initial play; do they negate the 3 baskets and the foul that came afterwards and restart the clock at the point where the foul should have been called?
Certainly, these are crazy hypotheticals, but I suppose that they're the very sort of problems that the league has considered in its slowly-evolving use of replay. And I think the league is right to be worried about those sorts of things.
I absolutely agree that missed calls are among the most frustrating aspects of watching NBA games. But then, so too are missed free throws and bad passes and poor decisions and sprained ankles and tendonosis.