I totally understand what you are saying and agree. Will just add a slight caveat that miranda protections (based on the Miranda precedent case) are not the same as 5th amendment rights against self-incrimination. Any statement made during the investigation (and prior to arresting the suspect and giving the Miranda) is going in your report and will almost certainly be used against the defendant at trial if it's incriminating. If you roll up on the scene of a DV and my wife is dead and I am covered in blood and the first thing I say when you see me is, "OH NO I KILLED HER!!!", that's 100% coming up in court despite me not being under arrest and miranda advisement when I said it.
Bear in mind, the vid I linked is a lawyer talking to law school students. Thing is, most people smart enough to understand how all this works and apply it in a smart manner are usually not people who routinely break the law and need to know this shit anyway.
It does apply in every day situations too though. Couple examples I can think of here in CA.
Beat cop pulls me over for speeding. Usually first thing out of their mouth is, "Do you know why I pulled you over?" This is a clear example of a seemingly innocent question designed to make the driver give up his 5th amendment right and admit guilt for what he's suspected of doing. Now you can handle this like a douche and say, "MY LAWYER SAID DON'T TALK TO COPS!!!", or you can be friendly and say something like "I am not sure officer, I was hoping you'd tell me." The latter statement is what I always say and it avoids confrontation while simultaneously preserving your rights.
Another example, usually the 2nd or 3rd thing out of the cop's mouth after you're pulled over is, "Is this your current address on your license?", or in my case, "Are you wearing your corrective lenses today?". Now in both cases, if I answer "no", I am going to be written up for additional citations. They're asking those questions specifically to get you to admit guilt so you can be written up for more citations. Even if they are correctable offenses, I'm still going to pay the $35 per offense or whatever correction fee is. In both instances, I am fully within my rights to say, "All due respect officer, but I'd rather not answer any questions today." Doing that would prevent additional citations if the answer happened to be no. However, if it were me IRL and the answer was no, I'd just lie and say yes. It sucks to lie but it's easier than dealing with cops who get annoyed when I try to assert my rights.
Another one that bugs me and I'll be honest, is hard for me to still be cool is when they ask on a routine traffic stop, "Where ya headed today?". That shit pisses me off to no end and when they do that, I usually respond with something like, "Is there anything else you needed from me today sir to complete the traffic stop?" That question is 100% geared towards investigation beyond the traffic stop.
