Depends on your local law, but in many, many places you cannot legally record a conversation you aren't a party to, even in public. In the US, in many states, it's not permitted to record a conversation you are a party to if others have not consented. There are various reasonable exceptions that permit recordings (e.g. public events, press conferences, trials, governmental meetings, recording interactions with police). "Conversation between two people happening in public" is not typically a permitted exception for recording.

Note that in this comment I'm talking about audio recording, which typically has much stricter regulations than video recording. I think the same principles should apply to video, and in some jurisdictions they do. But in my comment, I was using the laws around audio recordings vs physical eavesdropping to make an analogy about the problem of pervasive surveillance.