Actually, as the following Ngram Chart for the years 1980 through 2008 indicates, "walk the talk" (the grayish blue line) is considerably more common than "talks the talk and walks" (the regular blue line), "talk the talk and walk" (the red line), "walks the walk and talks" (the green line), "walk the walk and talk" (the yellow line), and "talk the walk" (the purple line) put together:

These results are for published instances of the various phrases in the Google Books database for each year, so it doesn't necessarily reflect the relative frequency of the various formulations in spoken English; but for published instances, the relative popularity of "walk the talk" is quite impressive. Evidently a lot of writers share the poster's opinion that "walk the talk" is a reasonable way to express the idea of "doing what you say you'll do or what you say you believe in."

I also want to support the point that 3nafish and Dan Bron make in their comments beneath the OP's question: It isn't illogical or beside the point to say that someone walks the walk and talks the talk (or talks the talk and walks the walk) because the implication in each case is that the person talks the appropriate talk and walks the appropriate walk.

Even "talk the walk" makes sense if you read it as meaning something comparable to the U.S. idiom "talk a good game"—that is, sound good but not necessarily do well. Many of the matches for "talk the walk" use that phrase in tandem with "walk the talk" to emphasize the value of communicating about what needs to be done before you shift to "walking the talk." But some of the riffs on "talk the walk" sounds like hooey to me, as in Karl E. Weick, Sensemaking in Organizations (1995):

To "talk the walk" is to be opportunistic in the best sense of the word. It is to search for words that make sense of current walking that is adaptive for reasons that are not yet clear.

I don't know about you, but I'm skipping that seminar.