It puzzles me why leftist parties don't all embrace lower taxes for the middle class.

They all do. My best guess as to why you'd say this is that you're including Democrats.

edit: Or, I could be a self-centered American that didn't consider others. I'll do better.

At risk of a strawman...

The shortest path to equality is to greatly reduce taxes on the middle class and increase them on the wealthy.

That's what's best for equality and for economic growth. Does this mean Democrats are horribly incompetent? Perhaps it's that equality and economic growth aren't their goals.