Why we can't use the same color in connected portions of planar graph?

We define the coloring of graph in such a manner that we can’t assign the same color to the adjacent vertices because if we give the same colors to the adjacent vertices then they are indistinguishable. Also note that we can give the same color to the adjacent vertices but such a coloring is called improper coloring and the way which we define the coloring is known as the proper coloring. We are interested in proper coloring that’s why all the books consider the proper coloring