No, we figured that out decades ago, which is why capitalism was generally abandoned in the developed world in favor of the modern mixed economy. "Capitalism" is now, though, used in at least three conflicting ways:<p>(1) To refer to actual capitalism (the real system dominant in the developed world in the late 19th and early 20th century, described and named "capitalism" by its socialist critics),<p>(2) To refer to modern mixed economies as opposed to forms further from capitalism, such as Leninism and its derivatives,<p>(3) To refer to a utopian realization of Econ 101 ideal markets, whose adherents seen to believe is actually a plausible economics system rather than a useful simplification in the same way as a friction-free model in physics.<p>The former, as mentioned above, cannot be redeemed, though a synthesis with other ideas is possible (and now dominant) that mitigates some of its worst elements.<p>The second may be improvable while still recognizably remaining a form of the modern mixed economy.<p>The third isn't realistic, much less redeemable.
What the free market rules should be are fairly clear. When corporations influence government to favor those corporations and blunt competition, that is not a failure of the free market, it is a failure of the government.