And I'm pretty far left, and have heard the same idea from other "lefties." Go ahead and cut the corporate tax to zero. The largest and most powerful corporations will bribe governments and set up special loopholes that work for them (but not smaller competitors) anyway. Level the playing field, as you say.
...and do away with special tax treatment of dividends and capital gains. Tax the owners of the corporations rather than the corporations themselves. This has a side benefit of no longer taxing investment income at a lower rate than actual earned income from working.