Q may not exist; but then again, neither does the Gospel of Mark - both are reconstructions; both are hypotheses.
That is to say, in New Testament scholarship, an exegesis of any given passage is laboring under a whole series of assumptions and hypotheses (most of them well founded) and ultimately raises a whole series of epistemological concerns: that Mark is the earliest canonical Gospel, that our understanding of Koine Greek is accurate, that what we call “Mark” represents a single text, and (most of all) that the textual reconstruction of Mark in the exegete’s Greek Bible is not simply a synthetic backproduct but corresponds more or less to the first-century original (autograph).
Thus, such skepticism regarding Q has something of the character of creationism in the context of academic biology. Hypothesis is piled onto hypothesis, although few would claim that efforts to classify a particular species are irresponsible or frivolous.
For the sake of laypersons who prefer traditional fundamentalist responses to the Synoptic Problem rather than weeding through the layers upon layers of scholarly discussion, such an position, while comfortable and placid, should be expected and is ultimately to be rooted in particular religious experiences, but, in regards to actual scholarly discussion of Q, the process of discussion will continue until better alternative hypotheses are formulated or until the hypotheses in use can be proven false.