We should take into account the semantics of the words "practical" and "application". For some students, practical is anything that will help them pass their exams; for others, anything that will come up in a job. In both cases, Automata Theory is very practical indeed.
As others point out, you will use grammars, for example, when studying compilers. But even more than that: understanding the whole concept of having different states and rules for transitions between them can make you a better programmer when you realize, for example, that your code is redundant here and there, and that when you improve it, you are applying in your code the same conceptual ideas behind DFA minimization.
Similarly for "application". What do you understand by that word? Even if you are a "down-to-earth engineer" you will see and use ideas similar to those of Automata Theory in real world projects: programming code, flow diagrams, and even the simple yet brilliant concept of a stack. For theory nerds like me, I consider applications of Automata Theory in other areas, like logic, algebra and finite model theory. Surely, I will probably never need to use the pumping lemma while shopping in a supermarket, but theorems like that have helped me understand the structure of certain classes of languages, not to mention the logics and algebraics structures they are in correspondence with. And that is something I value more than any measure of practicality.