This is untrue. In the heyday it looks like the 1% were paying about 7-8% more in effective taxes than today.

Take a look at this Slate article which includes data:

http://www.slate.com/blogs/moneybox/2017/08/07/the_history_o...

"So the real tax rates rich Americans paid in the 1950s may not have been so stratospherically high as some progressives assume. But they also may have helped create a more egalitarian society. That seems worth considering."

Mainly by removing the massive incentive for increased wealth past a tax threshold. 1% households back then made much less than today.