Art is a vast question of interoperation. The matter of whether it should be subjective or intentional is up to the artist. The beginnings of art had it be very subjective and intentional for a reason. Ideas and general information were present thru art as a means of communication. Little was imaginative because a cretin meaning was needed to be understood by many viewers. For this art was subjective, representational, and intentional.
Later art would become a medium for ideas, feelings, and human expression. Art evolved into a free-form medium for all to interoperate. Modern art does not have to be subjective and representational. It can be as free and belligerent as the artist chooses. Accidental art is a new happening as well. Works of artist like Jackson Pollok usually happened by accident and the artist found meaning in it after it was created. Abstract can work like this but it doesn’t have to. An artist can have the intention of creating a work that has no set form or structure. Or they might place balloons with paint inside on a canvas and throw darts to create a very drippy work (tons of fun). Whatever makes some one feel better is an art form is some aspect, it doesn’t have the be ideal or planned just as long as the creator feels something.