That's the same as one-party consent (that is, one of the parties having the conversation, not random passersby), which in the US applies federally as well as in about 3/4 of the states.

But most states - whether one-party or two-party - do not require consent to record a broad swathe of exceptions (particularly extortion, but not just that). Exact laws vary quite a bit - honestly one of the worst things about America is how different laws (of all sorts) can be in different jurisdictions.

Sometimes in a private conversation I will say things I would not want the public to hear me say. In places where there is one party consent it requires much more trust to have these types of private conversations, because any conversation could be recorded and placed on twitter.

For example, I think it's awful that in some places it's legal to privately tell you friend about a mental health struggle you are having, and for that friend to, without your knowledge, share a recording of that conversation with other people. In my mind two party consent is a basic data-privacy law. You cannot create a record of something you expected to be private. You can have an expectation of a private conversation to be private.