"The answer is simple. Eliminate the corporate income tax, and increase personal dividend tax rates to ordinary income rates."
This is already the case for many, many businesses.
"S Corps" (and other passthrough entities) are widely, widely in use and behave just as you suggested - the business pays no taxes, the monies flow to the owners, and the owners pay personal taxes on those flows.
It's very simple and it works very well.
It is not a fringe practice or a weird setup - almost every business you transact with is set up as a passthrough entity.
There is a catch...
A passthrough entity needs to pass all that cash through, more or less, inside of that tax year. You can't just sit on funds or store them up in your bank accounts or save for future R&D, etc. - you need to pass it all through this year.
And so if you are a mega-corp, that is a problem since there are many, many reasons you might want to store funds across several years ... and that is the class (C-Corp) that gets taxed.
So what you suggest is here, now. We, as a society, have decided that there is something negative about corporations slowly building up cash troves year after year without taxation and so we don't allow that. But I see they are doing that anyway, offshore, so perhaps it's time to rethink that...