I think people forget that corporate profit is not a bad thing. It leads to R&D, growth, and new jobs. Sure you could take all of that away from the bad corporations that make money. But honestly, is the average Joe really going to do as much with it. And lets really get realistic, is the government going to do anything useful with it other than to dangle it out as a carrot to the masses.
Corporate tax should be at zero. They pay all necessary fees (hidden taxes) and employment taxes. Everything else just gets added to their costs, and prices go up. If there is any way to make American companies less competitive on a worldwide scale, force their prices higher. This is the failure of the backwards thinking of the progressives. If American companies are making less money (or spending more on taxes) everyone loses out - including the government.
Corporate profit is a *wonderful* thing. In ways.
The attempt to make a profit, whether by an employee making a wage, or someone starting a corporation hoping for profits, it all is a force for making people do things that will make money, which in part is for the benefit of society. The farmer making a profit to grow and sell wheat, to a bakery who makes and sells bread, to the grocer who sells it to you at a nicely maintained convenient location, are all doing these things because they profit, which gives you a loaf of bread to eat.
Not all profitable activities are good for society. If the military-industrial complex uses its influence to start an unnecessary war that generates profit for itself (both for the war and for 'being prepared'), that's not good for society. If a drug company uses its influence to relax rules to let it market and sell an unnecessary if not harmful drug, that's not good for society. When the tire or oil industries use their money to buy out public transportation systems to create the car market for their products, that's not good for society.
Remember my nice simple wheat example above? The situation starts to change when you add in complexities, such as 'economic justice' for the labor who picks our fruit here - in the past, poor roving migrants of any race, currently more likely to be Hispanics, typically illegally here, pitting the low prices consumers want against the opportunities for the labor to make much income. It gets even more 'complicated' when you look at the history of imported fruit.
The United Fruit company in the past - like the 1950's and 1960's - was a very powerful interest in Latin America. It owned much of the production for the fruit industry that dominated many countries' economies. It didn't care for its profits that most of the people were in terrible poverty, if not the edge of starvation, as they got periodic work for the company - indeed, the poverty increased their profits. There was a need to keep the people from doing anything about that poverty and the excesses of the corporation, which meant controlling the government - and they did, paying large sums to the military regimes and other dictators who would use terrible violence to use killing and torture and threats against any potential political opponents - students, liberal politicians, labor leaders, left-wing intellectuals and others. The company would pay death squads at times who took part in this. The resulting tyranny did not matter much to them, because it was profitable. (The silence of the American people who enjoyed the, er, fruits of these policies are an issue of shame to the American system for their inaction and lack of concern, as well as the media to inform and the political leaders to provide the moral concern and influence public opinion).
What's needed is the balance between not too little corporate profit and freedom so that the productivity of useful goods and services for society isn't reduced, and not too much so that they become amoral tyrants above the people and untouchable by democracy, shifting back to when the people serve the few, rather than the other way around.
The right typically misses the side of this with the problems of 'too much power' for corporations. When they discuss the topic, they ignore the problems at the real situations of too much power, and instead use false analogies to the other side - 'the guy who grows our wheat needs the chance to make some profit' - as if the basic functions of the economy have anything to do with the issues with big business. Any restraint on mega industries is the same to some of them as putting mom and pop out of business.
In our democratic ideal, the people sort this out and decide where the balance should be drawn, rationally. But that's not how it works, really. There's a whole powerful mythology around the issues and a lot of bad information pushed out who serves someone's interest over the public. When the corporations 'hire' politicians who will support their interests, and the politicians needing the public's votes tells them things to make it seem like it's the public's interest, there becomes a feedback cycle as people fall for the myths.
Our early presidents noted the danger of powerful private interests becoming able to defeat democracy. The funny thing is, the result of that isn't a nation of furious people who are in rebellion against the powerful, it's a nation of people who are seduced to like the tyranny. We don't exactly have tyranny yet - in this country, we've exported plenty to other countries - but we have a lot of the conditions to keep moving that direction, including a public compliant to big business and massive control of our politics.
Yet things are not as bad as they could be - we still have voices, if not majorities, in Congress who are 'for the people' - the Bernie Sanders, Alan Graysons, and so on - who could be purged as our system now lets the big business interests target unlimited funds to removes its opponents.
To your point in the OP above, why should corporate taxes be passed along to the public to increase the people's taxes? 'Competitive interests' can lead to terrible extremes - 'how can we not let people earn 10 cents an hour, when the other countries offer corporations such low wages' - but it also ignores the advantages that come from investing the tax money - both in terms of competitive interests, and our own public well-being. The rhetoric from the right typically pretends the money is burned and had no benefit.
With that wrong ideology, of course they're 'right' in the wrong conclusion that it leads to to get rid of all taxes as waste. But it's not right.
We need to protect the interests of the American people - including the balanced policies allowing for the benefits of corporations but not the abuses.
I'd say we should also look to benefit the human race, as much as our political system is weighted for citizens 100%, non-citizens 0%. When we've bragged of being 'a leader in the world for freedom and democracy against tyranny', when we brag our economic system is better, those are good goals, but they include not just exploiting anyone else for our benefit.