We have a tag automata with a fair amount of questions (probably more where the tag is missing). Looking at them, it might as well be automata-theory (in line with graph-theory, complexity-theory, probability-theory, database-theory, ...).
But then, we have always made a point of not excluding practical questions, as long as they go beyond pure programming. Note that a similar discussion about graphs and graph-theory (which currently both exist) has not yet been resolved.
Can we expect questions that would be aptly tagged by automata and not by automata-theory? Do we want both tags (and retag theoretic questions to automata-theory), or only one? If so, which?