There isn't much juice to squeeze when you make one of the most progressive tax systems in the world even more progressive. Normalizing the idea that the middle class should pay very little tax makes it impossible to raise the necessary revenue as a matter of math.

AIUI, most EU nations (the ones with the great social benefits the left says it wants for America), have a flatter tax burden, where the middle class pays a higher percentage of the total.

Exactly. The tax platform that we need the most is that dentists are not paying their share. Penny-ante local landlords are not paying their fair share. There is too much focus on the ultra rich, you can and should take all their stuff but it doesn't amount to a whole lot.

Most people suggesting taxing the rich more aren't saying that the middle class should pay very little tax

how much of the revenue is necessary?