When one looks at works dealing with the Farrer Theory (FT) -- the argument that Matthew was used by Luke; thus dispensing with the hypothetical Q source -- one quickly notices that they are almost exclusively confined to articles and monographs attempting to argue for its validity and viability. When the NT student goes in search of works outside of the Synoptic Problem (SP) that utilize a working assumption of the FT, they are met with disappointment. It seems that the FT has failed to branch out beyond the specialization of studies on the Synoptic Problem. This conclusion could be faulty due to my limited exposure to the secondary literature, but this has been my observation.
In light of this observation, I notice two things the Two-Source Theory (2ST) has in its favor which the FT lacks: (1) a proliferation of works which assume the viability of a particular solution to the SP; and (2) to borrow the phrase from a comment on the NT Blog, the 2ST has a "sexier" title in 'Q' as opposed to the 'Farrer Theory'.
Now I must clarify what I mean when I say "advancing" the FT. By "advancing" I neither imply attempts at 'proving' nor the proposal of new arguments. Rather, what I mean is expanding the exposure of the FT beyond discussions confined primarily within Synoptic Problem circles and the meager (if any) reference to it in introductory textbooks.
Personally, I find theories and hypotheses which are named after their founders to be more than a touch trite. Theories such as the Theory of Gravitation or the Theory of Relativity seem, to me, to have more impact and stronger meme-potential than, say, if they were simply named Newton's Theory or Einstein's Theory. While in some cases the two examples are conflated (i.e.; Einstein's Theory of Relativity), for me it is the 'descriptive' part of the name that stands out and proves more memorable.
So what, then, is this all leading up to? I suggest that that (1) scholars who ascribe to the FT need to begin re-writing the story of Christian origins under the new paradigm that Luke knew and copied from Matthew. In short, to set the story of early Christianity in a world where Q never existed; and (2) I think -- with no disrespect to Austin Farrer -- the theory of Markan Priority without Q (aka the Farrer Theory) should be renamed, and that the new name should reflect what the theory is describing.
I read David Sim's article* in the latest NTS yesterday, which convincingly argues that Matthew intended to supplant Mark's Gospel with his own. Taking this as a point of departure, I think that there are a number of places where we can extend the argument to Luke on the FT. In this case we would see each successive gospel as a reworking and replacement of its predecessor(s). In light of this, I think proposing a "Theory of Gospel Succession" adequately describes what the theory attempts to explain (Matthew used Mark, and Luke used Mark and Matthew), as well as my developing view of the overall growth/evolution of the gospel tradition in the Synoptics (Mark wrote the first gospel --> Matthew wrote to expand, edit and replace Mark --> Luke wrote to edit and replace both Mark and Matthew).
*Sim, David C. "Matthew's Use of Mark: Did Matthew Intend to Supplant or to Replace His Primary Source?" New Testament Studies 57.2; 176-192.