You are factoring in the possession gain on offense but it doesn't appear that you are factoring in the opponent's loss of possession. For each turnover the opponent loses their average points/non-turnover possession (because points/possession already factors in the team's turnover rate and would artificially lower the points they miss out on when they do in fact turn it over) and we gain our average points/possession, no?

It's more complicated...

**TDLR: If you treat a forced turnover as adding your teams average points per possession and subtracting your opponents points per possession, you're doing it wrong.**
For example consider a 2 minute game where Team A starts with the ball and the average possession is 20 seconds long if no turnover is forced.

Team A would have 3 score-able possessions at shot clock times 2:00-1:40, 1:20-1:00, and 0:40-0:20.

Team B would have 3 score-able possessions at shot clock times 1:40-1:20, 1:00-0:40, and 0:20-0:00.

If Team B forced a turnover 5 seconds into the game:

Team A would have 3 score-able possessions at shot clock times X2:00-1:55X, 1:35-1:15, 0:55-0:35, and 0:15-0:00.

Team B would have 3 score-able possessions at shot clock times 1:55-1:35, 1:15-0:55, and 0:35-0:15.

So both teams still have equal score-able possessions but one of Team A's duration was reduced by 5 seconds (the time into the possession they were turned over). So unless Team B forces the turnover right at the end of the first 20 second duration, they don't gain an additional scoring opportunity. If you extend this over a 40 minutes game, the average duration of each scoring opportunity is not going to be exactly 20 seconds, so the first turnover may or may not actually change the number of scoring opportunities either team receives or even the duration of time for those scoring opportunities.

Another scenario, If Team B forces a turnover 5 seconds into the game, Team A forces a turnover 5 seconds into Team B's second possession, and Team B forces a turnover 5 seconds into Team A's 4th possession:

Team A would have 3 score-able possessions at shot clock times X2:00-1:55X, 1:35-1:15, 1:10-0:50, X0:30-0:25X, and 0:05-0:00.

Team B would have 3 score-able possessions at shot clock times 1:55-1:35, X1:15-1:10X, 0:50-0:30, and 0:25-0:05.

This is more interesting, if the total duration of the elapsed time before turnover is less than 20 seconds (the average possession duration) as in this scenario, and the delta in turnover is 1 or less, there are no additional scoring opportunities generated. However, you can see that if the time elapsed before turnovers had totaled 20-40 seconds Team B with their additional forced turnover would have 1 more scoring opportunity than Team A (and the duration of that opportunity would be 0-20 seconds depending on the time elapsed prior to those turnovers). If the turnovers added up to 40-60 seconds though, the teams would again have the same number of scoring opportunities.

3 turnovers per 2 minutes is a pretty high clip. That's 1.5 per minute or equivalent to 60 turnovers in a 40 minute game... A typical game has closer to 25 forced turnovers or ~6 turnovers per 10 minutes.

If Team B forces turnovers the first 4 times that Team A holds the ball, and Team A forces a turnover only the 2nd time Team B has it (all turnovers taking place 5 seconds into the possession) and we extend the game clock to 10 minutes:

Team A would have 13 score-able possessions at shot clock times X10:00-9:55X, X9:35-9:30X, X9:25-9:20X, X9:00-8:55X, 8:35-8:15, 7:55-7:35, 7:15-6:55, 6:35-6:15, 5:55-5:35, 5:15-4:55, 4:35-4:15, 3:55-3:35, 3:15-2:55, 2:35-2:15, 1:55-1:35, 1:15-0:55, 0:35-0:15.

Team B would have 16 score-able possessions at shot clock times 9:55-9:35, X9:30-9:25X, 9:20-9:00, 8:55-8:35, 8:15-7:55, 7:35-7:15, 6:55-6:35, 6:15-5:55, 5:35-5:15, 4:55-4:35, 4:15-3:55, 3:35-3:15, 2:55-2:35, 2:15-1:55, 1:35-1:15, 0:55-0:35, 0:15-0:00.

Obviously turning your opponent over 4 times more often is great but in this scenario it only resulted in 3 additional score-able possessions over your opponent (which is roughly equal to the margin of forced turnovers you get, but not exactly since if the shot clock were 15 seconds shorter in this example, it would have only been an extra 2 possessions as explained by the earlier examples).

**TDLR: If you treat a forced turnover as adding your teams average points per possession and subtracting your opponents points per possession, you're doing it wrong.**