We'll have to agree to disagree. I don't think "time to react" is relevant. The vast majority of the players in the league are trying their best all the time, not "reacting" to the score. So when the points are scored isn't important, IMO, only that you score the most in total.
Time To React has no bearing on how hard people are trying. It's how many shot attempts you can realistically get off in a period of time. At its core, basketball still has a lot of chance in it. Most of the skill is making the odds more in your favor (a short shot is generally more likely to go in than a long shot). So, the more chances you have to hit a shot, the more likely you are to finally hit that shot. On defense, slowing the other team down and making them shoot a low-percentage shot is as important, since it reduces their opportunities to score. So, given that your team is trying their hardest the entire game (they are), the number of possessions becomes important.
If you get a large enough sample size, teams score points in a pretty linear fashion; the lumps all smooth out at a distance. But when you zoom into a single-game or single-quarter level, the progression is lumpy. There's streaks of made shots and of missed shots. There's several of these in every game. Very rare is the "average game" where Team A scores at Rate A linearly, and Team B scores at Rate B linearly. Ties and lead changes abound in a close game. Sometimes, big leads (8-12 points), and sometimes several of these.
Now, knowing that progression is "lumpy", and the risk of a slump always exists, imagine taking the sample size down a notch to a 6:00 block. A slump in this block can lead to big run by the other team, who is taking advantage of your inability to score simply by scoring normally. Combine that with (horror of horrors) a streak by your opponent, and you can have a big swing in points.
Because the game is slump and streak, having another 6:00 block in front of you to shoot your way back into the game (and to give the other time a chance to "cool off") is nice. A couple of missed shots by your opponent, a couple of made ones by your team, and the score is close again. Streak and slump, slump and streak. It's not that your team isn't trying, it's that they're in a slump. Or conversely, they're not trying harder, just taking advantage of a streak.
If there's no 6:00 block in front of you though, there's no opportunity to streak if you're slumping. So what happens? The coaches play hard against the odds. Make it so that the shots are as low-risk (or high-reward) as possible; usually this means waiting until the defense makes a mistake, and driving in for a hoop and harm. A made bucket and a foul is the Holy Grail of risk/reward: a close-in shot that could be worth 3 points.
Anyway, the last 6:00 is important for two reasons: it's the last, and scoring is not perfectly linear; it's lumpy.