Also, an up front request for immunity is a massive red flag that says "I'm probably involved in the illegal thing, or some other illegal thing", which is not h

Also, an up front request for immunity is a massive red flag that says "I'm probably involved in the illegal thing, or some other illegal thing", which is not how you want to introduce yourself to a police officer, especially if you're not a serious suspect at the time. Even if the cop could grant it, why would he? Obviously different if your lawyer says that requesting immunity might work, probably because you're knee deep in someone else's mess and their experience tells them that prosecution will be far more interested in your testimony against them than stuff you might need to admit to.