That wasn't the plan at that point, those plans only came to be when Volgin used the davy crocket in the chopper, and even then she had to get the philosopher's legacy first.
but why did the boss even need to do this, i mean she could have thrown snale off from the bridge without breaking his arm, why was there even a need for this? The boss was a motherly figure for snake after all.
It makes her defection look more real. Later in the game, even Volgin is a little scared to question her loyalty. He had to talk to her like an equal, rather than him acting like her colonel.