Huh? Variance is the spread so I assume you are talking about variance in shot location (I cannot imagine what other variance you might be referring to in this context). The wider the spread the fewer the shots that go through that little hoop thingy. When the ball doesn't go through the hoop it counts as a miss, and due to annoying little rules of math that are impossible to break, misses always bring the percentage down.
variance in a mathematical context are influenced by the sample size. And fewer free throws/game results in a smaller sample size and the smaller sample sizes increases the variance and makes free throws a bigger luck affair.
Lemme give a quick example:
Let's say Trey Burke is a 80% free throw shooter.
In an imaginary particular game he is fouled once while attempting a three pointer, getts three And-1 foulshots and 7 normal shooting fouls that result in 2 attempts each.
That's a total of 20 foulshots in the current format. On this night, he misses 4 attempts.
The first foulshot after the 3 pointer misses, and 3 more attempts on standard shooting fouls. Overall he's extracting 16 points out of his fouls shots.
When you award only 1 shot regardless of the value of the shot, he would be shooting 11 times that night.
He misses 2 shots which results in a > than 80% conversion ratio. As I already mentioned he bricks his attempt after his 3 pointer and another one on a 2 pointer.
Now he sinks 6 six of his free throws that award 2 points and 3 that award 1 point. That results in 15 points out of these attempts, even though he has an above average free throw shooting night.
Now transfer that on a whole team. Things like fouls at 3 pointer are so rare over the course of a season that you'll have problems getting the luck out of these attempts for individual player.
Also there's research indicating that the 2nd free throw attempts are 3-4% more accurate than the first overall for athletes shooting multiple shots. So you rob them of a warmup which will devalue 3 point free throw shooting.
So they'll have to ask themselves is the time gain worth adding randomness into the game or is it even wanted to randomize outcomes?
I personally think the best way to influence game length would be removing the gestures to indicate fouls. NBA refs have voice comm and communicate this way with the technical staff while preparing the next inbound play.
The number of available timeouts and duration of these is also a big reason for delay of play. These changes could cut off as much time as could reducing the number of foul shots at least the way I perceive time during a game.