So I was asking my wife the other day how often 日本人 use the full passive-causative grammer point, and she told me she never uses it in real life daily conversations, but I was wondering if other people had any different experiences.
Is it rarely used or is it something that you more so read in books?
Are you making me answer that?
You’re being made to answer it! 
To OP: Wish I had more insight, but I guess your wife is a native speaker (right?) and so knows much better than I do!
Short answer, it’s used all the time.
Long answer, most native speakers in almost any language will not have an active awareness that they are using specific structures unless it is pointed out to them. As an example, when I first came to Japan, part of the training I did for teaching English was speaking without using idioms. Almost everyone in the workshop thought that they use idoms maybe once or twice a week. The teacher then put people in groups and made us talk about random stuff. The class used over 100 idioms in a period of less than 10 minutes.
This is not to say that you will hear it every day, but you will certainly find yourself confused quite often when you need to understand it and aren’t used to those types of sentences.
It’s so difficult to get people on the same page when you talk without using idioms.
People always get the wrong end of the stick when you start talking without idioms.
This is a really fun anecdote haha, it’s always interesting to take a moment and reflect on your speech patterns and those of the people around you.
In a slight inverse to this, I’m teaching English oral expression courses atm to university students where I’m living and I’ve made it kind of a game with my students where I try to use a lot of idioms during our convos and then I’ll “pop quiz” the class to see if anybody can guess what I meant. It’s a tough part of speech for foreign language learners fs but so fun to play with.
How about fitting an English idiom into a faux-Confucian (孔夫子) idiom, while simultaneously exhibiting the specific grammar point under study?! 
(@jrmr50 @bunnypro, too!)
How often do you say “I was made to do something” or “I was allowed to do something”? That’s how often you’d need to use the passive-causative. As Asher said native speakers don’t realize what grammar they use most of the time but also it depends on a person’s situation. A low-level employee or a student probably uses it all the time while a president of a company probably rarely gets to use it.
From my limited experience talking with my teacher, there are certain causative-passive phrases which get used very frequently and unconsciously in conversation. 待たせられた comes to mind.
Basically, how often are you talking in everyday conversation about things you’re forced to do? Fairly rarely, but when you are, there’s no other choice.
In science writing (like, for experiement write-ups or scientific papers) in English, you’re supposed to use what’s called ‘past-passive voice’, like, “The acid was mixed into the solution,” instead of something more active, like “We mixed the acid into the solution,” or even “The acid mixed into the solution.”
I wonder if there’s a similar science-writing style for Japanese science writing, like maybe as taught in say a Japanese high school chemistry class. And I wonder if it would use the Japanese passive-causative specifically? Or what?
Maybe that whole ‘past-passive voice’ thing is just an English convention, or a Western European convention? Dunno. But would be interested if anyone knows.
Google Translate gives a stable (round-trip) translation of “The acid was mixed into the solution.” to 「酸を溶液に混合した。」 Hmm, doesn’t seem to even use ‘passive’ form, but it does translate directly back into the identical English. Hmm, maybe this is an example of what Cure Dolly refers to as the ‘zero ga’, or ‘∅ が’, where only を (object) and に (target) are used in the sentence, and the subject (normally marked by が) is just implicitly assumed to be ‘we’ (or ‘I’).
Interesting question - a quick Google suggests that in Japanese the non-past is used and the passive is only used as it might normally be used. I could only really find examples of elementary and middle school writing though or just science education writing rather than formally written results. I will ask a science teacher when I get to work though.
The passive voice is used a lot more liberally in Japanese literature than in English literature, I believe. It has a different feeling compared to English, I think, but I am nowhere near well read enough in Japanese to speak with any authority.
Please don’t forget someone is still doing the action when the sentence is passive - it is not intransative. Compare:
[誰かが]酸を溶液に混合した。—> [Someone] mixed acid into the solution.
酸は[誰かによって]溶液に混合された。—> The acid was mixed into the solution [by someone].
Note: によって is used since に is already used for 溶液に but it can sound quite emphatic normally.
Well, actually, this version is what I was referring to with the ‘∅ が’ mention. The subject (inferred by context; often defaults to ‘I’ or perhaps ‘we’ in a scientific paper; could be ‘誰か’ as in your example) is omitted, but still ‘there’, hence the ‘hidden’ or ‘zero’ ga, or ∅ が, so like:
[∅が]酸を溶液に混合した。
And this is translated by GoogleT to “The acid was mixed …”. Now, that is passive-voice in English, and in English it also has a hidden subject (the experimenter). But it didn’t come from the passive-form (of a verb, not a ‘voice’ necessarily; from recent rabbit-holing I seem to recall that in grammar these are two different kinds of ‘passives’ (but maybe not!)), i.e. with られ. I’m not referring to so-called ‘transitivity’, namely 他動詞 and 自動詞. I just mentioned the ∅が idea to help me guess where the structure of the GoogleT translation came from.
It could be that the GT translation automatically switches from passive voice (in English) to active voice (in Japanese; but with the active subject hidden by ∅が), simply because that’s how such sentences get translated in practice. And that such practice might simply be because of stylistic differences between science-writing in English (past-passive voice) vs. Japanese (active-voice, but ∅が).
[Here and there, I’m probably confusing between passive voice and passive verbs, as this is something I only sort of read about in passing on a rabbit-hole dive through Wikipedia/etc. Or indeed, I might just be mistaken overall about this alleged distinction. Apologies if any confusion, and feel free to set me straight.]
I guess the analog to passive-causative in English might be more like: The acid was made to mix into the solution. ??
I live in Japan and I wouldn’t say I hear it all the time. However, it is used frequently enough that you need to quickly identify the grammar point in your head to understand what the speaker is saying.
It’s vital to understand causative, passive, and causative-passive because it will make it clear who or what the subject in a sentence is. I still often get lost listening to Japanese daily conversation because I can’t quickly pick up on the grammar in my head to identify the subject, even if I know the meaning of the words in the sentence.
Also, I asked this same question to my Japanese co-workers and they had no idea the causative-passive was a thing, then I explained it using the easy example 母は私に食べさせられました。Then they’re like “oh yeah we do use that a lot.”
I am aware although from the perspective of a native speaker the subject is not really “null” but simply implied - the problem we have here is we have contextless sentences. Kinda semantics at this point though. I think the reason Cure Dolly stresses null subjects so much is because it is not an intuitive concept for English speakers. Despite what she says about “learning Japanese as it really is” or whatever her course is very much designed with English speaking students in mind.
In a passive sentence the subject is the patient (the thing/one receiving the action, marked by が in Japanese - は is also obviously possible here as in my example sentence). You are talking about the agent which is not the subject of a passive sentence. The agent is a so-called indirect agent so takes に. As I mentioned since に was already used (to mark a target/indirect object) によって was used instead but in a model passive sentence it goes [patient-subject]が[indirect agent]に[passive form of verb]. In English the “doer” is also an indirect agent and not the subject - the same things apply although in English word order and an optional subclause/adjunct using the preposition “by” is used instead of case marking particles. I.e., "[patient-subject] is [verb’ed] by [agent].
I suspect this to be the case as the lack of agency doesn’t require the passive voice in Japanese, I believe. The passive doesn’t sound as…passive in Japanese, I suspect. Basically, I think you may be onto something although I am reticent to say anything more until I speak with a native speaker about it (which I will try to do today).