Well golly, let's not let facts get in the way of a good story. The federal government had a huge debt to pay down after the war. The debt as a fraction of GDP spiked to an all-time high after WWII, and steadily declined until the late 70s. The higher taxes were going toward that debt.
Then we dramatically cut taxes in the late 70s, and the debt started climbing again.
Granted, but if spending had otherwise returned to the previous levels then that debt would have gone away entirely and then the new taxes along with it. That rather obviously didn't happen. :)
A now-deleted sibling comment linked to the corresponding spending levels, which confirm the continued spending (note that this graph doesn't even include the debt): https://upload.wikimedia.org/wikipedia/en/0/05/Us_gov_spendi...