>>22928067No.
You're forced to take fighting, ground, and either ghost or dark to hit Normal, electric, and ghost types.
To hit fairy you need either steel or poison, and since ice and rock are already covered, poison is the obvious choice.
You're still left with water, ice, ground, flying, bug, and dragon, and no type hits all of these supereffectively.
And this isn't even taking into account dual type pokemon.