The notion that sounds carry inherent meanings certainly figures in folk ideas about language; it somehow matches many people's intuitions. But a non-arbitrary connection between sound and sense obviously violates some principles of modern linguistics.
There is lots of research being done right now, but it often involves an acknowledgement that the phenomena are underdeveloped and/or not accepted in mainstream linguistics. Also, we should distinguish between a universal, interlinguistic sound-meaning connection and merely intralinguistic patterns. The former seems hard to defend, but ideas about synesthesia may be reopening the question. The latter seems to be cropping up in a large number of articles.
This answer may change further if curiosity leads me to keep prodding the subject...
The article for phonesthetics (or "sound symbolism") indicates that it's a very old question. But in the "modern" part of that article, the story seems to peter out in the 1970s and '80s.
However, a simple search ("phonoesthetics", "phonestheme", "sound symbolism", "sound semantics" in scholarly articles, book reviews, and conference proceedings) using the University of Toronto catalogue suggests that the situation is the reverse. The research is accelerating:
Here are some of the article titles:
Ideophones, Interjections, and Sound Symbolism in Seediq (Lee 2017)
The Case for Sound Symbolism (Nuckolls 1999)
The Specificity of Sound Symbolic Correspondences in Spoken Language (Tzeng, Nygaard & Namy 2016)
Sound-symbolism: A Piece in the Puzzle of Word Learning (Parault & Schwanenflugel 2006)
Sound to meaning correspondences facilitate word learning (Nygaard, Cook & Lamy 2009)
Sound Symbolism in Basic Vocabulary (Wichmann, Holman & Brown 2010)
What is the link between synaesthesia and sound symbolism? (Bankieres & Simner 2015)
Several of the 20 or so articles that I checked have decent numbers of reads, downloads and citations for the field (ranging from a half-dozen to a few dozen). Tellingly, however, almost every abstract includes a line qualifying the phenomena as "not widely accepted", "contradictory to the principles of linguistics", or "not yet well understood or explained".
The abstract of Nuckolls' 1999 review says this:
The proposal that linguistic sounds such as phonemes, features, syllables, or tones can be meaningful, or sound-symbolic, contradicts the principles of arbitrariness and double articulation that are axiomatic to structural linguistics. Nevertheless, a considerable body of research that supports principles of sound symbolism has accumulated. This review discusses the most widely attested forms of sound symbolism and the research programs linked to sound symbolism that have influenced linguists and anthropologists most. Numerous reports of magnitude sound symbolism in the form of experimental studies and comparative surveys have been integrated into a biologically based theory of its motivation. Magnitude sound symbolism also catalyzed a number of experimental studies by psychologists and linguists in search of a universal sound-symbolic substrate underlying all languages. Although the search for a sound-symbolic substrate has been abandoned, the success rates of these studies have never been satisfactorily explained. Sound-symbolic processes have had a definitive impact on morphological analyses of phonesthemes and on historical linguists' understandings of diachronic processes. A typologically widespread form of sound symbolism occurs as a kind of lexical class known as the ideophone, which is conspicuously underdeveloped in standard average European languages, and highly perplexing for linguists and anthropologists. Although it has always been a respectable domain of inquiry in ethnopoetics and interpretive ethnography, the case for sound symbolism has of late been argued with renewed vigor on the part of psychological anthropologists and philosophers who see a paradigm shift under way.
I find this telling: It's not necessarily linguists who are the most curious about sound symbolism nowadays, but anthropologists. And it's not so much digraphs that hold interest, but ideophones (more or less onomatopœia).
One thing I will suggest is that popular conceptions of phonesthetics are based on poorly defined criteria. One question is what happens when we find counterexamples. Take the notorious glitter, glisten, glow, gleam, etc. idea. How about glad, gland, glutton, glacier, glitch, globe, gloat, and glob, which have nothing to do with light or vision? Do they matter and if so to what degree?
Perhaps unclear questions like these are why practitioners of the increasingly scientific field of linguistics feel the need to apologize for their interest in the phenomena, even in the abstracts of papers studying them. (Incidentally, I don't think there are many ancient ideas about language that would still be studied today without an apologetic tone.)
One direction of possible interest for the cross-linguistic non-arbitrary hypothesis is psycholinguistic.
A well-known experiment involves the bouba/kiki effect. In short, speakers of many languages associate the nonsense word "bouba" with rounded, cloud-like figures but "kiki" with spiky ones. Synesthesia appears to be involved.1
In a similar vein, the Bankieris & Simner article above includes these highlights from the abstract:
- We tested synaesthetes’ and controls’ ability to determine foreign word meanings.
- All participants correctly identified some word meanings at above chance rates.
- Grapheme-colour synaesthetes performed significantly better than nonsynaesthetes.
- The same cross-sensory integration driving synaesthesia may underlie sound symbolism.
- Synaesthesia endows/co-occurs with enhanced multisensory skills in unrelated domains.
The work on this question is recent and has potentially plausible mechanisms underlying it, so watch this space.
1 Though one could imagine that other factors are involved. For example, in English the shapes of the letters that make up these words could bias round/spiky associations. A person could visualize the letters even without seeing the word written.
Thoughts on inter- vs. intralinguistic patterns
My own thoughts: I find the subject interesting as regards sounds' perceptual value.
I always think of an anecdote of my mother's. She spent some time in India in her youth, and one day asked a man what he thought was the most beautiful word in Hindi. He immediately answered: "The word for 'lady': begum!" Savouring the word, he repeated: "Begum!"
The usual response to this story is laughter. Why? Because to a North American English speaker, no word that sounds like begum could mean "lady". This tells us two things: One, that intuitions about which sounds have which meanings are not universally shared interlinguistically. Two, that there is nevertheless some intralinguistic consistency.
To poke more holes in the interlinguistic hypothesis: Find someone who doesn't speak a language that you do. Ask them to guess the approximate meanings of ten words (not cognates of ones they know). The study on synesthesia I quoted mentions that people guess word meanings correctly at above-chance rates. My own anecdotal evidence suggests that they don't have a chance when the question is open-ended, testing between the utterly unrelated Hebrew and English.
But I do believe in the effects within a language. Even if people don't have intuitions about the meanings of digraphs like gl- or sn- (at least I don't), speakers of the same language do share vague affective perceptions like those about begum — or about bouba and kiki, for that matter. And you can create new words with fairly reliable categorizations, at least if you make the categories as extreme as opposites. How many English speakers would fail to categorize Galadriel and Mordor correctly into good and evil?2
The Wikipedia article mentions that phonesthetic phenomena may be due to priming, which makes sense to me. Even if there's no reason why a woman should be called a begum or a lady, once a language settles on one or the other, speakers may make similar judgements about other words using the same sound configurations. The first connection is arbitrary, but later words can be derived from or influenced by it. Over time, perhaps that could even account for a tendency — far from a scientifically predictable rule — for phonological clusters to form semantic patterns.
2 When the categories are arbitrary, opinions become unreliable. I wonder how many of us would disagree with Monty Python's sorting into "tinny" and "woody" of gone, newspaper, litterbin, sausage, antelope, seemly, prodding, vacuum, caribou, leap, and bound?