You misunderstand the rights you have.
I lived under full out communism, you don't even know what sort of oppression the "show me your papers" phrase represents.
I think the "Show Me Your Papers" meme is more about people being randomly stopped for no reason just to be ID'd. I'm sure the Soviet Bloc abused this to no end.
Sure there are bad apples and on a slow day you might have to ID yourself. But I'd wager the MAJORITY of the time, it's not worth getting into it when you are pulled over or questioned.
Walking down the sidewalk not causing any harm? Eh, if you wanna fight that fight go for it, but I think it makes it worse.
I was in NYC back in the day with stop and frisk, got frisked, that's a little extreme but look at what happened when they got rid of that.
If the police show up to my door asking for ID or to do a breathalyzer, (happened in Australia), then no way, I'll decline.
It's totally normal to be required to ID yourself when you're committing no crime
Sure, technically, but you are just adding fuel to the fire, and when outgunned with a guy with cuffs and all kinds of power and people backing him up, that's the wrong battle to choose IMHO.
If the cop is doing this for whatever reason, they know they are wrong, on a power trip, or just looking for someone. Giving an ID might just satisfy that ego or rule you out as the guy the police are searching for. Even when stopped and frisked in NY, I was not ID'd. I have never been ID'd randomly. These are outlier scenarios that should be carefully navigated because you can avoid or attract a lot of trouble.