What are the arguments that support assumption of potential of earth to be zero.

According to the definition of potential of earth work done to bring a particle from infinity to a place. Considering earth work to bring particle from earth to a particular place as potential of earth of infinity is 0, similarly potential of earth is 0.

Potential energy and potential are just relative terms since you measure it assuming potential of infinity is zero. Instead of that you take potential of earth as zero to be reference level and change the potential of all other bodies accordingly.

If potential at infinity is taken as zero, then potential of earth cannot be zero. It has to be -GM/R where M - mass of earth, G - universal gravitational constant and R - radius of earth.

It seems that the original question was about the electrostatic potential of the earth and not the gravitational potential.

Treating the electrostatic potential of earth as zero is mostly an arbitrary choice. Take a different reference, and the electrostatic potential of earth may not be zero.