Because Hermione was always the one, who did not pursue power tools. She wanted to live peacefully, far away from all the danger.
The Invisibility Cloak, as the Ignat used it for, was to protect himself and his family and not a tool for power and violence.
The reason why Hermione chose the cloak is pure logic and logic alone, and the story of the three brothers only reinforces that which can be figured out purely by logic.
What's the ring good for? Nothing really. It can't really bring back the dead only their spirits who apparently grow tired of being summoned back to witness the living, and there is some ...
Hermione has always been an objective individual
I think her preferred Hallow was a symbol of the type of person she is. In some sense, both Harry and Ron gravitated towards the Hallows that addressed some deep personal issues of their own (Ron's insecurities and Harry's great losses). In comparison, Hermione was someone who preferred to make her decision ...
Hermione is correct, it is obvious from the tale which gift is best.
The brother who got the wand was killed the night after he boasted of the powerful wand.
The brother who got the stone soon killed himself.
The brother who got the cloak lived a long life and died in peace.
And then he (the younges brother) greeted Death as an old friend, and went with ...
According to the subtle laws governing the ownership of wands - To win a wand, one must overpower and hence defeat its master in some way.
"Subtle laws govern wand ownership, but the conquered wand will usually bend its will to its new master." —Garrick Ollivander
So, the 3 ways possible to win a wand's allegiance from his old master are:
Steal the wand