I know, I pointed in another thread that people's opinions are more strongly rooted in emotions than in facts. The media does play a strong part in shaping perception though, and once a worldview has been internalized, it becomes "emotional" and harder to change (though by no means impossible). It's just a sad aspect of human psyche.
You can make sales tax that don't hurt the poor too much (VAT tax from where I am, for example, depends on the kind of item : food has low to no tax, books have low tax, luxury goods have high taxes).
A flat tax can't, because it's inherently unique (if not, it's not a flat tax anymore).
Also, wealth redistribution is necessary - unless you just want to end up with a very few people hoarding the entire wealth and everyone else with nothing. The US already are at a point, WITH progressive taxation and some measure of wealth redistribution, where 1 % of people own over 30 % of the wealth. Does that sound normal or desirable to you ?
---
Also, BTW, about media leaning,
here is a website that ranks them according to their political bias :
View attachment 708873
I don't know most of them, but about those that I know, it seems pretty correct to me.