The edited question raises some further points that I think can only be covered by putting forth a speculative theory of how English speakers understand tautological attribution, which doesn't really fit into my already-too-long initial answer, so I'm going to do that here. I have little theoretical justification and no empirical justification for this theory; it's more just to show how you could explain these facts.
Is there a salient difference between "tuna fish" and "oak tree"?
Let's compare them.
- "Tuna" is a kind of fish or fish meat; "oak" is a kind of tree or tree wood. Not much difference there.
- Both "tuna" and "oak" can be used in ways that feel like noun compounding: "tuna melt", "oak grove".
- Both can be used in ways that feel more like adjective attribution, but with the sense of "tuna-like" and "oak-like": "tuna flavor", "oak finish".
- Only "oak" seems to have uses that feel adjective-y, while also using the "of oak" rather than "oak-like" sense. In fact, even "oak finish" can mean "a finish that's oak-colored because it's made of oak wood".
So, what difference could this make?
Well, we seem to be happier to extend "X tree" to new trees a lot more than "X fish" to new fish. If you've never heard "beechnut tree" or "trout fish" before, I suspect you'd accept the former while marking the latter as weird. This is something that could be tested by gathering a bunch of speakers and a bunch of examples—you could even do psycholinguistic surprise-measure tests. Of course I haven't done any such tests, but let's assume that it's true.
So, what could explain it?
Let's start with Peter Culicover's Construction Grammar-style view of the lexicon and semantic processing, as described in the books ''Simpler Syntax'' and ''Grammar and Complexity''.
When you hear "oak tree", the syntax-semantic interface ends up activating the generic attribution construction in the lexicon, which applies "oak" to "tree", and flags it as redundant. But, at the same time, "oak tree", as a cliche, has its own node in the lexicon, which isn't flagged as redundant, and which overrides the generic construction. So, you understand it as a perfectly normal bit of English, and don't notice any redundancy (unless you think about the words consciously).
What happens when you hear "beechnut tree"? The same generic attribution construction activates the same way. There is no "beechnut tree" cliche to override it. But memory isn't a hash-table-style exact associative lookup, it works by analogy. And "beechnut tree" is similar to "oak tree" and "ash tree" and a bunch of other things, similar enough to activate them to some tree.
If the total activation of this cluster is strong enough, your brain sees "beechnut tree" as something that should have an analogous node: this is an English cliche that you just didn't know. If it isn't, as with "trout fish", the generic construction takes effect, and you get a "redundancy asterisk" in your conscious understanding of the phrase.
So, why would this happen for "beechnut tree", but not for "trout fish"? The difference isn't really a rule, it's the result of a process similar to the kinds of determinations that a multi-level neural network makes.1 So, factors like how "nice" of a pleonasm "oak tree" is, how "adjective-y" the "beechnut" node is, how many "X tree" cliches you have stored, how often you hear them, etc. all come into play in an analog computation that either does or doesn't reach a sufficient threshhold.
Over time, the clusters of related cliches that languages grow will be partly just a matter of chance, and partly a matter of non-linguistic factors (do English speakers have reason to talk about kinds of trees more often than kinds of fish?), but also partly determined by linguistic factors—the fact that "oak" can be used adjectivishly more easily than "tuna" only matters because English has an adjective+noun construction that's more productive than noun+noun.
And you'd expect both the nonlinguistic cultural factors and the linguistic factors to be different for Thai speakers than for English speakers.
Unfortunately, I know little about Thai, but let's compare Japanese and Spanish to English.
In Japanese, nouns being used as modifiers need a special particle—but it's a fully productive construction. Plus, many words that tend to be adjectives in other languages are nouns in Japanese, even ones rarely used outside the modifier construction. So, the fact that "oak" is sort of adjectivish shouldn't matter at all, and all tautological attribution cliches should be very "nice", so it should be much easier for the pattern to spread to new idioms. It might even generalize to the level where we'd call it a semi-regular construction, or even to a productive one that can be applied anywhere.
In Spanish, on the other hand, you can't modify nouns with nouns except for a very restricted, non-productive set. Instead, you're usually forced to use prepositional constructions (like "the fish of the tuna" as opposed to "the tuna fish"). Those are less likely to be stored as idioms, so you'd expect Spanish to have fewer "tuna fish"-style cases, and to be much more resistant to forming new ones.
Again, I haven't done any research to see whether these expectations are true, but let's pretend I did, and they are. So then, you could look at Thai and make some predictions about how freely it accepts "tuna fish" style pleonasms, and see if those predictions are right. You could then apply similar reasoning to other pleonastic constructions. If it all works out, instead of a vague sense that "Thai seems to allow more redundancy than English", you'd have a catalog of the kinds of pleonasm that Thai and English each tend to allow, and how freely each language allows them.
But again, I haven't done all that work. All I can do is show that it makes sense for English and Thai to differ in the kinds of pleonasm they allow and how freely they allow them, for (at least partly) linguistic reasons. And that it's at least plausible that the contrasts you were asking about are real, and can be explained, but don't have a single simple explanation.
1. Of course at the bottom level, your brain is such a neural network. But this is probably a few levels higher than that, and we manifestly do have rule-like as well as network-like reasoning at that level. In particular, the syntax-semantic interface that gives us "modifier + modificand" and the semantic processor that therefore applies the modifier to the modificand are rule-like.