Why don't coaches call a time out in that situation

you dont call a TO on the rebound, you call a TO once james pulls up and doesnt shoot. to answer your question, i dunno

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You're more likely to score if you don't call timeout. Main reason is because it's tougher to score against a set defense, and calling a timeout allows defenses to do that.

You never call timeout there.

No timeout was right call. Calling a TO after Harden picked dribble up would also be a mistake because you'd have to inbound the ball and they could just deny Harden with a double all while having their D set.

really it's harder because offenses have to stop and then inbound 4 against 5 in the halfcourt

but the stats that say it's easier to score without a timeout might not fully take into account the end of a crucial playoff game

Several reasons. Don't give defense a chance to set up and situationally substitute. Most teams, and I would think all teams, work on just such in game situations all the time, and should know what to do without a time out. Don't have to sweat getting the ball inbound at half court which often seems problematic for teams.

We're so conditioned to expect time outs, but I've always thought the better play is no time out.

I heard a former hoops coach recently saying the hockey coach at his school would laugh at him about all the time outs in basketball. "Don't you guys ever practice?" he would ask all the time.

No timeout is the correct move. Not only is it easier for houston to score on the break, but harden was a lot more likely to get a foul called in transition then against a set defense. Once harden picked up his dribble and passed to Dwight at the 3 point line the game was over. Even if mchale calls a timeout there golden state is able to regroup and set their defense. I doubt mchale expected harden to do what he did.