Recording conversations

I see that police across the country have taken to arresting people for recording police activities in public, using the states' laws against recording conversations unless all parties agree.

Usually these laws are applied to telephone conversations, but they also apply to any conversation.

I've always been opposed to these laws against recording conversations.  It seems to me that if there's a later dispute as to what was said in a conversation, particularly in the course of a lawsuit, then a recording would remove the "he said. she said" difficulty of resolving the truth.  In effect, the laws against recording conversations are a license to lie.

(The cynic in me suspects that legislators passed these laws with a view to protecting themselves from being held accountable for what they may have said on one occasion, and then wanted to deny later.)

I don't understand the "invasion of privacy" argument.  The communication is being made - the person being recorded knows s/he's talking to the other person, even if ignorant of the recording.  How is his/her privacy being invaded?  Perhaps people think that publishing or broadcasting the recording would be an invasion of privacy;  it may well be, but how would that be different from a person publicly recounting a private conversation that hadn't been recorded?  If there is harm to the person whose words are being broadcast, the harm is the same whether a recording or a transcript is being made public, and the same remedies would apply.

So repeal the "license to lie" laws!