> I believe that in the UK, Canada, Australia you have the right to remain silent
In Australia, not always true. You have no right to remain silent if questioned by an Examiner of the Australian Criminal Intelligence Commission (ACIC), a rather Star Chamber-esque federal law enforcement agency tasked with investigating terrorism, organised crime and other “major crimes” (a rather ill-defined category; pretty much any murder investigation could be given that label if they wanted to, although most murders wouldn’t interest them.) However, while they can force you to answer questions, they aren’t directly allowed to use your answers to prosecute you (but they can use them to prosecute other people, and they may be able to use them against you indirectly, if your answer leads them to discovering new physical evidence or witnesses.) You have the right to a lawyer, and the lawyer is allowed to object to questions, but you still have to answer them-if they object, they can attempt to get a court order after the fact to stop the answers from being used, if your lawyer doesn’t object at the time a court can dismiss an application for any such order on that basis. Also, if they call you in for questioning, it is a crime for you to tell anyone except for your own lawyer that they are questioning you.
> The right to council is often for the trial, not telling you how to avoid answering questions during a police interview.
It is important for the interview too. One’s lawyer can object to leading questions. They can give advice on how best to answer questions-you can be telling the truth, but some ways of phrasing the truth can sound much better than others. They can give advice on when it would be best to exercise one’s right to silence, and when it might be better not to.
Sometimes it even just serves to scare the police off. One guy I know was a bit of a hothead when he was younger, ended up in a fistfight, he put the other guy in hospital. He claimed self-defence, and it was one of those iffy “Who started it? Did he use excessive force in defending himself?” cases. He swears the only reason he wasn’t prosecuted, is he turned up to his official police interview with this really expensive, locally well-known criminal lawyer, and that scared the police and prosecution off, he was never charged. Who knows, but he’s probably right. Probably there’s some other guy out there who was in a similar situation, whose parents couldn’t afford that kind of lawyer (or didn’t know who they were or where to find them), and ended up being charged, going to trial, maybe even convicted, or talked into pleading guilty for a lesser sentence.