Why doesn't Stockfish (DroidFish) try to flag me? Imagine the following position: 

 [FEN "3k4/7p/7K/3B4/8/8/8/8 w - - 0 1"]


White is played by Stockfish in DroidFish and black by human (me). We both have 15 seconds.

After a few moves, white bishop or king gets the black pawn and... "Game over,draw by impossibility of mate!"... It is logical, due to the fact that there isn't mate position with two kings and one bishop.

I repeated the experiment sometimes and the same result happened... So, I wonder, why doesn't Stockfish flag me? Isn't it smarter to wait 50 moves for drawing with the hope to flag me without getting the pawn? 

There are many possible mate positions without getting the pawn. I imagined one if pawn is promoted to knight and then: white king g3, white bishop h3, black king h1 and black knight f3. Black to move. Black knight to g1 and white bishop to g2 checkmate.

 [FEN "8/8/8/8/8/5nKB/8/7k b - - 0 1"]

 1...Ng1?? 2. Bg2#


So, it is not more logical in these cases, engines to try to flag the opponent? Maybe in a game between two engines it is meaningless, but in the case of engine vs human, I think it isn't so illogical.

What is your opinion?
They are programmed to play the best chess, and there is simply no programming added in that attempts to account for the opponent being low on time. The way it played it was the best chess-wise. A human might try to flag you, but not the computer. Personally, I like it that way.