You could ask why do zoologists and biologists study chromosomes? or why do geologists take core samples. It is the duty of scientists to expand human knowledge and understand, and stellar parallax is a way of understanding how the heavens work. Some have said "in science, there is only physics, All the rest is stamp collecting". Which is true in a way. We dont NEED to know how far stars are, and we dont NEED stellar paralax, but in the quest for knowledge, we WANT to use it. Most of what we figure out in science is unimportant, but sometimes someone figures out a theory of relativity or a standard model of quantum mechanics, it might not be important to most of us, but it is there, and it is pretty cool. As for practical applications, perhaps we want to know which stars are closest, so we can send a probe towards them. Or maybe stellar parallax can tell us more about redshifts. Maybe it's just a fun way to figure the motion of the galazy.