Ballots are meant be a private matter - a whole lot of shite happens when they're public knowledge - so while people can choose to do so, the media pushing for people to list how they voted in anything seems like a very risky idea and pretty unethical to me.
Also, that would out any immigrants who didn't have the right to vote. Not sure where your sympathies lie there, but I'm not going to put people at risk when there is rising xenophobic attacks in many areas, just so someone can decide how they should feel about someone's problems.
I personally have very little sympathy with those Remainers and in certain political parties who continue to think just shouting how evil and thick and unworthy of consideration the other side is is any sort of political argument. As unbeneficial as Brexit is, that shite is just another flavour of us vs them that doesn't do anyone any good either. It didn't help any of them win and it isn't helping anything now.
Can I ask what the remain side lied about? Genuine question.
The government that was the main campaigners for Remain lied for years about certain things being the EU's fault that actually they could have done many things about but chose not to do so because it didn't suit them. They did pretty much nothing during the campaign to deal with that damage, I don't recall any discussion of what they would do other about any of the things they blamed on the EU other than 'we can change the EU more from the inside' which was the wishywashiest bullshite that I don't know how they thought it would convince anyone.
I had Remainers tell me that the government didn't need to really campaign because it's the status quo which I think is more them lying to themselves that preaching to the choir was enough.