We're starting from the position that, absent a public safety concern, the defendant's right to know his rights is greater than the law enforcement interest in not encouraging the defendant to exercise them, and if the cops don't read the Miranda rights then the statements aren't admissible.
Now throw in a public safety issue -- the cops have to interrogate this guy or some people could get hurt. Why does that change the result? If the public safety issue is more important than reading the defendant his rights, then it's also more important than allowing the police to use the defendant's statements in court, since we've already decided as between those things which is more important. So the consistent outcome should be for the cops to interrogate the defendant and resolve the public safety issue, but for them not to be able to use any of those statements in court.
Is there some non-obvious reason for it to not work that way?