Don't you find it rather convenient that she had no support? People just kind of left her alone even knowing she was going crazy? None of the men paid her any mind, cast her off, and in your scene, Gertrude doesn't want to see her and makes short shrift of her. She literally had nothing to hold on to even if she'd wanted to hold on.

Last, and as much containing as all these,
Her brother is in secret come from France;
Feeds on his wonder, keeps himself in clouds,
And wants not buzzers to infect his ear
With pestilent speeches of his father's death;
Wherein necessity, of matter beggar'd,
Will nothing stick our person to arraign
In ear and ear. O my dear Gertrude, this,
Like to a murdering-piece, in many places
Gives me superfluous death.

Funny that, the "ear and ear" part and talk of "like to a murdering-piece"; where have we heard of that before? :-) and to think Claudius' speech all started with:

Follow her close; give her good watch,
I pray you.

and then somehow that didn't happen and she was able to "wander off" and drown herself which, under the circumstances, is suspicious in how she did it all by herself?