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I've heard this claim a lot, from Chinese teachers in real life, and on this Wikipedia page, where the claim "At present, more than 90% of Chinese characters are phono-semantic compounds" lacks a citation. It seems reasonable, but I can't find any real evidence to back up this claim.
Is this number one of those popular urban myths, or is there a factual basis to it?
It is actually not possible to provide an unambiguous statistic like this without either being ignorant of the complexity of character development, or pushing some kind of agenda. Victor Mair and John DeFrancis have been spouting this kind of idea for a long time, but I suspect that they've either (1) focused too much on lexicography and not nearly enough on paleography to make such a conclusion, or (2) wanting to blow up the significance of spoken language and diminish the role of written language in the history of a language's development.
In real life, characters are not cleanly divided into the liushu categories, and the classification is quite deficient to fully describe many characters. 90% seems like an overestimation, but one can actually arrive at this number by interpreting any character with any amount of history of involvement with phonetic components, no matter how slight, as a "phono-semantic compound". However, if someone follows this interpretation, it is misleading to use vocabulary from liushu (like phono-semantic compound) to describe these characters.
There are example of characters (e.g. 「源」, 「採」) being both compound ideograms and phono-semantic compounds, as categorised as a type of the latter, but there is rarely an obvious mention that it is a type of the former as well. There are also non-obvious cases; for example the characters「喪」and「鬱」, under an opaque interpretation, can both be described as "phono-semantic compounds" (and indeed have been in traditional sources):
Nobody recognises the phonetic components in these anymore, as they are either very rare components or have been graphically corrupted too much over the years, but they're categorised as "phono-semantic compounds" anyway. I personally find such a liberal interpretation as bordering on meaningless, as it is equally possible to provide a liberal interpretation of "pictogram", "ideogram", or "compound ideogram" to misleadingly inflate a statistic.
I find what @droooze wrote is interesting, but also incomplete, and sorry but "90% seems like an overestimation" is the description of a feeling, not a citation of evidence.
I think that many people will agree to answer your question as, roughly, "a majority of characters used in modern Chinese are made up from recurring parts, of which typically one hints to the very broad meaning or semantic category (of which there are but a few hundred), and one other may be understood as a mnemonic for the sound (the reading) of the character, with varying degrees of accurateness, and not infrequently clustering around more than a single 'type' of syllabic setup (of these sound-indicators, one of my sources (school material, 3900 characters listed) has around 750)."
@droooze is quite right in that many characters that have been or should be characterized as containing one or more parts that hint at the character's reading are either (1) not classical and straightforward 形聲字, or (2) have lost the utility of a 'plain' 形聲字 to the modern speaker due to historical sound changes, or are (3) just too obscure or too rare to be a useful, practical (as opposed to 'originally created as') 形聲字 in an operational sense.
So no, this is definitely not an urban myth; there are many, many false assertions floating around when it comes to Chinese language and writing, but this is not one of them. To establish reliable figures, though, is quite a bit harder; let me just ask you, before you even start counting, what is it you're asking for: the number of phono-semantic compounds in the totality of all Chinese characters? or only those as used on in mainland China? in Taiwan? the proportion of phono-semantic compounds among all (repeating) occurrences in typical modern texts?
Worse, how will you go and count, say 工 gong as it appears in 貢 gong, 江 jiang, 項 xiang, 紅 hong, 扛 kang, 邛 qiong? That 邛 'is' a phono-semantic compound may indeed matter very little to people who struggle with this character's unusual structure, rare occurrence, and aberrant reading!
