The whole premise of "don't talk to the cops" is one of risk management. Don't be confrontational, don't try to outwit them in an argument, don't show off how smart (you think) you are, etc. Be nice, be meek, be quiet. You lose nothing if the cop is a good cop and you reduce the risk of losing everything if the cop is a bad cop. Leave the lion-handling to the experts, i.e. your laywer, who isn't you, who can say things you can't, and who hopefully has many years of experience in knowing how to negotiate with the police.
Obviously (well, hopefully) your kid running away or your house getting burgled are situations where "call the cops" trumps "don't talk to the cops". YMMV.
I've a couple of friends who are cops. It's not (generally) that dangerous physically, compared to some jobs, but it is dangerous mentally - a few years of being a cop and the world starts getting divided into "perp", "vic", "witness", "suspect", etc. And it starts creeping into their social life. It's a monochrome perspective that no amount of increased pay can solve, and I'm very much in favor of giving cops generous leave entitlements instead - indeed, mandating an amount of leave every so often - as much for society's benefit as their own.