I totally agree with this analogy, though maybe to add some nuance (or pedantry), I'd claim that to start learning Chinese, you need to pick a modern dialect (probably Mandarin), which is like choosing Spanish over Portuguese or Catalan. Then, learning Japanese or Korean (or Vietnamese) is like learning a nearby but non-Romance language that was heavily influenced by Latin or Romance languages, like English. Knowing Spanish will let you appreciate the similarities with English, but you'd still need to delve into historical Spanish (or French) to really see the connections.
Chinese is a pretty old and continuous language, so at the advanced level, learners could delve into Classical Chinese, which is truly analogous to Latin, and was also a dominant lingua franca in written form across East Asia. Pieces of Classical Chinese are 'alive' in everyday use, kind of like how Latin is 'alive' in the Romance languages through general and obvious similarities, or specific vocabulary, (e.g. "quid pro quo", "ad hominem"). But Classical Chinese is radically different from any dialect of today's vernacular Chinese.
In any case, the similarities and overlap definitely make learning between CJK(V) easier!
100% agree with this post, which I tried to get at saying that Korean and Japanese are distinct. Apologies for not making that clear. Your post is great to clarify this all more specifically.
The cultural side of things definitely requires a lot of time. And that’s fun.
What also takes time is learned how ideas are shared. Not just grammar, but which version of the multiple correct grammar options that is more common. How are paragraphs constructed? What is usually shared first in an idea or argument versus the end?
You can have someone with completely correct grammar and pronunciation that sounds odd to a native speak because the cultural / idea organization is not “native”.
Go back to middle Chinese, of which, for example, the Shanghai based Wu dialect, or the Southern Teochew dialect, retain much of the features of, and you will really feel like you're studying the mother language.
Chinese is a pretty old and continuous language, so at the advanced level, learners could delve into Classical Chinese, which is truly analogous to Latin, and was also a dominant lingua franca in written form across East Asia. Pieces of Classical Chinese are 'alive' in everyday use, kind of like how Latin is 'alive' in the Romance languages through general and obvious similarities, or specific vocabulary, (e.g. "quid pro quo", "ad hominem"). But Classical Chinese is radically different from any dialect of today's vernacular Chinese.
In any case, the similarities and overlap definitely make learning between CJK(V) easier!