These are a thing. Have you studied 四字熟語 (よじじゅくご) yet? Literally “four character idiomatic expression”. For instance, 一期一会 (いちごいちえ), “one life, one encounter”.
But there are shorter and longer expressions, like 如是 (にょぜ), “as it is”.
Or 本来無一物 (ほんらいむいちぶつ), “originally there was not one thing”.
It is wonderful to just stumble on words that put meanings together in interesting ways. This is one of the delights of kanji.
Didn’t get to those yet. I see japan as a secluded island where a lot of knowledge didn’t have time yet to wither but not small enough to be forgotten by hardships.
There are threads here devoted to yojijukugo. Also, they appear on Japanese proficiency exams. Older Japanese people complain that the younger generations are not learning them.
To be fair though, I’m not sure that 心配 is, strictly speaking, structured as advice. It comes from 心配り (こころくばり), which is “thoughtfulness” or “taking care of.” Over time people adapted the onyomi to it. It’s a description of an action, but there’s no real “call to action” as far as I can tell.
Bonus for people who are interested in jukugo etymology, usually when a character is composed of one character representing an action, and one character representing the object of that action, they will be in that order respectively (着席 arrive > seat, sit down; 登山 climb > mountain, mountain climbing). The above mentioned transition from 心配り to 心配 is why 心配 breaks this rule of thumb.