To go on a bit more about this point, semantic-phonetic composition (形声) is very important, much more important than knowing all the original radicals (at least for comprehension of the actual kanji).
The semantic part (often on the left), is usually the radical of kanji which are of this type. However the phonetic part, which is just as important is usually not a radical, so if you just concentrate on classical radicals you will miss a lot of information; which is why you should also consider a more broad idea of what a radical, or a “consituent part” of a kanji is.
For example take the series of kanji:
工 - construction
江 - creek (semantic on the left: water)
紅 - crimson (semantic on the left: thread/textile)
虹 - rainbow (semantic on the left: insect??)
功 - achieve, success (semantic on the right: power/ability)
All of these are read the same (こう), which is indicated by the presence of the 工 phonetic (功 is somewhat of an outlier, because the phonetic part is on the left, but I would still consider it 形声).
I am still regularly learning new kanji in a structured way, and I can skip thinking about half to 2/3rds of the onyomi, simply because you can infer it by this kind of rule.
Almost all of these kanji have the semantic component on the left, and the phonetic component on the right.
(One exception of a phonetic which is always on the left is 芻 (すう), occuring in 芻, 雛 and 鄒; and a semantic which occurs on the right only is the one occuring in the last kanji of these, the large village/building radical - if someone knows another phonetic only ever occuring on the left, I’d be interested )
One caveat is that one phonetic might indicate more than one reading, or that the reading used to be according to the phonetic, but it has changed over time. (also two on’yomi might’ve been borrowed from China at different times, f.e. 経 being read けい (Tang dynasty borrowing) and きょう (earlier borrowing, thus mainly read this way in Buddhist words like 経典 (きょうてん) - sutra, scripture))
For example consider the phonetic 乍, occurring f.e. in
作 - make (さく, さ)
昨 - yesterday (さく)
詐 - deceive (さ)
酢 - vinegar (さく)
You can see that this phonetic is both read さ and さく, and you’ll have to remember which is which.
More information about 形声文字 can be found on the following sites:
形声文字 - Kanji with a semantic and phonetic component - Morg Systems (also has a lot of other blog posts about kanji topics)
https://archive.is/f4ww4 (article by the Nanbanjin Nikki linked in the blog post above, has great information about phonetic series, which one to learn and so on - the links of that article seem to be dead though)