NavyUmp,
I was trying to explain why the rule makes the batter out on a TSNC if 1st is occupied with less than two out. If the batter weren't out in this situation, then R1 would be forced to second. So a catcher could intentionally drop the ball at his feet, throw to second for the force on R1. There would be still plenty of time to get the B/R, with the throw to second taking about 2 seconds, and the relay to first about 1.3 seconds. So if the rule didn't declare the batter out on TSNC with R1, less than 2 outs, a double play would be likely.
This isn't some theory; the original rule was that the batter was "bound to run" if the pitch wasn't caught on the fly or first bounce (no gloves back in the mid 1800's). But catchers would intentionally drop the ball and collect double plays. The rule was changed to stop that.
Same thing for the IFF. Before 1890, popups often led to double plays. The first incarnation of the IFR declared the batter out with only R1 rather than R1 and R2, but that was an over-correction. The batter's only responsibility is to run to 1st, and on most popups he can get there before a relay throw. R1 and R2 of course would both be in a quandry whether to try to advance or retouch. So a double play would be likely with the IFR.