Your post pretty much sums up the reason you go for two in that situation. If you go for two and miss with 4 minutes left, you know that you need 2 more possessions (so if you get the ball back, you know that you can settle for a long FG and try another onsides kick). If you wait until late to go for 2 and miss, the game could be over at that point without enough time left to onsides kick and go for the FG. My strategy will change if I know I need one more score vs. two more scores, so it's helpful to know how aggressive I am with my play calling (and how aggressively I need to conserve time).
There is no reason to believe that going for 2 after a second TD is more likely to succeed than going for two after the first TD...so the question becomes, is it better to know how many scores you still need now, or later. The old school reasoning is "make it a one score game", but there is a big difference between a 7 and 8 point game. I'd rather enhance my chances to win the game, rather than "extend the game".
As I mentioned, you see more and more coaches realizing this is the way to go (just as you are with the coaches beginning to go for 2 when they are down 14 and score, since it increases your chances of winning).
Here is a pretty old article about it as the analytics community was starting to realize that it's the right strategy (it's the first one I found when googling, but I'm sure there are others that go into more details that I can get into in a post)...
Let’s start with the obvious: your odds of winning when trailing by 15 in the 4th quarter are really, really low. From 1994, the first season the two-point attempt was introduced to the NFL, to 2011, 68 teams have entered the 4th quarter trailing by exactly 15 points. Only one of those teams...
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