I couldn't find the position on Sensei's library with the search position function, so I used the MoyoGo pro game database. In the majority of the pro games I checked A was immediately played by black. This was around 75% of all games, but there was still a large amount of pro's that didn't play the move, but attacked in sente somewhere else first, and came back to it later.
As I'm probably somewhat weaker than you are, I could be way off the mark here, but I think it's a question of the balance of territories. The A you proposed is a very big move for black, but it's solely territorial, and definitely gote. So I think that if it doesn't put you behind in the game, it's a way to simplify the game, which is a good thing I believe. In this game however, I think you are already behind in territory, so I don't think that is an option.
I also have a question about Black B: it seems like a severe attacking move. Would it be possible to play one line higher, on the fourth line, to combine attacking and building the right side for black? playing just one or two moves there, then coming back to A would still leave black behind in secure territory, but put him ahead in influence. Or do I have the wrong idea here?
$$W
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$$ | . X X O . . . . . . . . . . . X . . . |
$$ | . X O O . . . . . . . . . O . . . . . |
$$ | . X X O . O . . . O . b . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . X . . |
$$ | . O X . . . . . . . . . . . . . . . . |
$$ | . O . X . . . . . . . . . . . . . . . |
$$ | . . O X . . . . . . . . . . . . . . . |
$$ | . . O , . . . . . , . . . . . , . . . |
$$ | . . . . . O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . X . . . . |
$$ | . . . O . . . . . . . . . . . . O O . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . O . . . X . X . . . . . X O . . |
$$ | . . . . O X X . X . . . . . . X O . . |
$$ | . . . . . O O X . . . . . . . . W . . |
$$ | . . . . . . . . . . . . . . . . . . . |
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- Click Here To Show Diagram Code
[go]$$W
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$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . X X O . . . . . . . . . . . X . . . |
$$ | . X O O . . . . . . . . . O . . . . . |
$$ | . X X O . O . . . O . b . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . X . . |
$$ | . O X . . . . . . . . . . . . . . . . |
$$ | . O . X . . . . . . . . . . . . . . . |
$$ | . . O X . . . . . . . . . . . . . . . |
$$ | . . O , . . . . . , . . . . . , . . . |
$$ | . . . . . O . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . X . . . . |
$$ | . . . O . . . . . . . . . . . . O O . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . O . . . X . X . . . . . X O . . |
$$ | . . . . O X X . X . . . . . . X O . . |
$$ | . . . . . O O X . . . . . . . . W . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
As to how to deal with the white ikken tobi on the lower side, there were three answers that occured in pro games:
$$W
$$ | . . . . . . . . . . . . . . X . . . . |
$$ | . . . O . . . . . . . . . . . . O O . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . O . . . X . X . . . . . X O . . |
$$ | . . . . O X X . X . . . . c . X O . . |
$$ | . . . . . O O X . . . . . . W a O . . |
$$ | . . . . . . . . . . . . . . . b . . . |
$$ ---------------------------------------
- Click Here To Show Diagram Code
[go]$$W
$$ | . . . . . . . . . . . . . . X . . . . |
$$ | . . . O . . . . . . . . . . . . O O . |
$$ | . . . . . . . . . . . . . . . X . . . |
$$ | . . . O . . . X . X . . . . . X O . . |
$$ | . . . . O X X . X . . . . c . X O . . |
$$ | . . . . . O O X . . . . . . W a O . . |
$$ | . . . . . . . . . . . . . . . b . . . |
$$ ---------------------------------------[/go]
1) The sequence Black A, White B, Black C
2) Just Black C (white often leaves the position for another part of the board at this point)
3) Tenuki. Not defending the territory in the first place seems to provoke this response quite often from pro's in this position.