Oswald T. Allis in "The Five Books of Moses" (3rd ed 1964) attacks the DH and defends the traditional view. In this book, he addresses the Sinai-Horeb issue. His general argument is that J and E get really fragmented if one tries to separate them, and he is right. Advocates of the documentary hypothesis note this as well. If the only sources were J and E, the theory would be considerably weaker. But we also have P and D and they break more cleanly.
Let's look at his argument in detail. In making a more general point (that there are sometimes variations in wording within a single source, even though one would expect uniformity) (p. 34), Allis includes an endnote (p. 310, n. 27), where he discusses Horeb and Sinai:
If Horeb is regarded as characteristic of E (Ex. iii.1, xcii.6, xxxiii.6), the mention of Sinai six times in Ex. xix constitutes a serious difficulty, since all critics apparently find a considerable E element in this chapter. According to Driver the verses which mention Sinai are either P (vss. 1, 2a) or J (vss. 11, 18, 20, 23), while vss 2b, 3a, 10-11a, 14-17, 19 are given to E. . . . But this analysis destroys the continuity of both E and J. E.g., E skips from Ex. ii.14 (or 10) to iii.1 and then to iii.4b.
Let's unpack this argument. Allis argues that if we separate E and J using the Horeb / Sinai distinction, we run into a problem with the story in Exodus 19 (were God revealed himself just before giving the Ten Commandments). More specifically, once we separate out the J and P elements from the story, we are left with an incomplete E narrative.
Allis uses Driver's breakdown of the sources. However, as I have noted, Friedman later revised this breakdown slightly and reverses some of the J and E sources. (See my Exodus comparison chart --- good thing I put that together.) Friedman's E story coveres 19:2a-9, 16b-17, and 19.) (This argument is easier to follow with an open Torah.)
How does this argument hold up? P is not a problem. The P source is simply the introductory sentence 19:1, and R has 19:2a.
E and J are a little messier, but not too bad. They are interwoven, but E stands in pretty good shape. God talks to Moses (19:3-6), and Moses tells the elders and the people (19:7-8), and then God speaks again to Moses and tells him he will appear in a cloud (19:9). And the God does so. (19:16b-17, 19.) Driver's version (see the chart) is a little shorter and choppier, but still hangs together as a coherent story.
J also holds up. In it, God tells Moses to tell the people to get ready (19:10-13) and he does so (19:14-15). On the third day, there is thunder and lightening, smoke, and God appears and speaks to Moses again. (19:16a, 18, 20-25.)
So Allis's more general point is one worth considering and I think it is one that is universally acknowledged. If separating the sources produces incoherent or incomplete stories, that weakens the claim for the DH. Conversely, if separating the stories produces complete and coherent stories, which are themselves inconsistent with other narratives, that strengthens the claim. But everyone acknowledges that separating the sources sometimes produces complete and consistent narratives that are themselves inconsistent with other narratives (like the two creation stories), sometimes produces messier fragments, and sometimes produces something in the middle. And I think everyone acknowledges that this is more of a problem with J and E, and less of a problem with P, E, and JE.
But here, once Friedman's revisions are taken into account, the E source is fragmentary but not incoherent.
So I will keep this argument in mind as we go through other sources.