What follows is really a methodological question with a long introduction.
I think it rational to question the nature of the significance of the many cognate parallel word pairs and even triplets between Biblical Hebrew and Ugaritic that Dahood gathered. I even think it rational, in individual cases, to question their very existence. But I think it irrational to think that the phenomena is without at least some significance.
A fairly large set of similar parallel cognate word pairs between Akkadian and Biblical Hebrew also exists. But there are also rather obvious semantic parallel word pairings. Akkadian ḫadû // râšu as a parallel to Hebrew חדה // שמח in Jeremiah 31:13 may be a case in point. Ḫadû and חדה are both cognate and have approximately the same semantic ranges. Râšu and שמח are not cognate but share overlapping semantic ranges each with the other and with ḫadû and חדה. Tawil, 379, explains the diverging semantic development of Hebrew שמח and its Akkadian cognate šamāḫu, “in Akk. ‘grow > flourish > prosper > be proud’; in Heb. ‘be high > shine forth > be happy.’” On the question of the semantic equivalence of Akkadian ḫadû and râšu, consult STC 2 op l 57 r. ii 21ff (CAD R, 209),
LI = râš[û]
LI = nag[û]
LI = ḫid[û]
Dahood (1972), 354 (#550), documented an apparent relationship between Hebrew חדה // שמח in Jeremiah 31:13 and Ugarit *šmḫ // *ḫdw in KTU 1:3 V:21-22 and possibly KTU 1:18 I:8-9 (the text is broken).
Let’s look at an Akkadian example from BMS 6:97-132, one of the witnesses to Meyer’s Shamash #1. Line 129 reads,
šamû liḫdūka erṣetim lirīšk[a]
May the heavens rejoice in you [Shamash], may the earth be jubilant in you.
In the Jeremiah passage, YHWH “will gladden them (נחמתים) and cheer them (שמחתים).” “Them” refers to YHWH’s people. In contrast, in line 129 of the prayer to Shamash it is the heavens and the earth that rejoice and are jubilant in Shamash. But the heavens and the earth compromise all that exists. While not part of the context of Jeremiah 31:13 specifically, in Akkadian, as well as Ugaritic, Phoenician (KAI 27:13 for example), and Aramaic, the juxtaposition of the cognates for “heavens” and “earth” is common in Biblical Hebrew. It is interesting that non-Semitic languages also juxtapose “heaven(s)” and “earth” but this fact may not be to the point I want to make here.
A couple of methodological questions with introduction and postscript: Assuming that our desire is to show some kind of cultural interaction between those who spoke and wrote in Hebrew and those spoke and wrote in the various dialects of Akkadian (or Ugaritic or anything else), how much methodological control do we lose at the sentence or a few sentences level when we venture beyond cognates? On the other hand, in the light of semantic development within the individual languages, do (some) cognate markers actually provide only the perception of methodological control without providing actual methodological control? For larger blocks, like flood stories and historical accounts, their many common markers seem more or less unproblematic; small blocks of material with few markers or even possible false markers certainly have their methodological problems.
Dahood, Mitchell, “Ugaritic-Hebrew Parallel Pairs,” RSP II (1975), 1-39
Mayer, Werner, Untersuchungen zur Formensprache der Babylonischen „Gebetsbeschwörungen”, Studia Poul: Series Maior, 5; Rome: Biblical Institure Press, 1976
Tawil, Hayim ben Yosef, An Akkadian Lexical Companion For Biblical Hebrew: Etymological-Semantic and Idiomatic Equivalents with Supplement on Biblical Aramaic, Jersey City, NJ: KTAV, 2009