The first and most important insight here is to recognize that burden of taxation (the incidence) need not fall on the entity taxed. Economist Herb Stein is famous for having quipped (on the subject of the corporate income tax):
"...that it’s as if people think that if the government imposed a tax on
cows, the tax would be paid by the cows."
Are Taxes on Corporations Taxes on People?
The corporation may front the money, but ultimately that money comes from customers, employees, vendors, creditors, and equity holders. Miller and others have written down models where corporate shareholders bear the burden but it doesn't have to be that way.
So to assess the consequences of eliminating the corporate income tax, we really want to know who pays (bears the burden of) the corporate income tax. To the extent that it is the providers of capital of the firm who bear the burden, we might assume that lowering the corporate income tax would act like an income tax cut for the rich. But there are simple models where customers pay some of the corporate income tax, such as if domestic and foreign products (as well as investments) are perfect substitutes, then (immobile) labor pays all the burden of the corporate income tax. Unfortunately, the issue of incidence remains murky despite decades of work on the subject.
Regardless of who pays, it is clear that enormous resources are devoted to corporate income tax avoidance probably because corporations have so many more opportunities for tax avoidance than individuals do, due to their complexity, multi-territoriality, and general scale and scope. If eliminating the corporate income tax freed most of those resources invested in corporate taxation preparation and avoidance (on the order of \$150 billion by two estimates just in compliance costs, ignoring strategically wasted resources), resources amounting to something like half of actual corporate income tax revenue would be usable for other activities. Free up those resources and you can make everyone better off, at least in principle. You might for example create a revenue neutral increase in dividends, capital gains, and interest taxation to offset the corporate income tax cut. This could leave beneficiaries of current spending essentially unaffected while the holders of current capital in taxable accounts would be a bit worse off and tax-free accounts (retirement, charities) slightly better off from the direct effects of the tax changes. But since their compliance costs fell massively, there might be enough to make everyone better off.
The bottom line is that that the corporate income tax is a expensive way to gather tax revenue from rich people and we are not sure it even does get money from rich people. The corporate income tax can plausibly harm non-rich people in the process. Taxing the income of the rich directly, if that is the end goal, is much more efficient. The resulting efficiency gains can be split between the rich and poor. Even if you don't particularly want to tax the rich, a more efficient tax policy means tax rates can be lowered. So there is something for a liberal and conservative economist alike to love with this tax reform.
Here are a couple of papers that suggest that higher corporate income taxes induce corporations to have more debt and less equity (greater leverage), although there is some evidence that reducing these taxes would not reduce leverage in the short run.
...low tax rate firms lease more, and have lower debt levels, than high
tax rate firms
Debt, Leases, Taxes, and the Endogeneity of Corporate Tax Status
The results suggest that taxes have had a strong and statistically
significant effect on debt levels. For example, cutting the corporate
tax rate by ten percentage points (e.g. from 46 to 36%), holding
personal tax rates fixed, is forecast to reduce the fraction of assets
financed with debt by around 3.5%
Do taxes affect corporate debt policy? Evidence from U.S. corporate tax return data
...we show that taxes have a first-order effect on capital structure.
Firms increase leverage by around 40 basis points for every
percentage-point tax increase. Consistent with dynamic tradeoff
theory, the effect is asymmetric: leverage does not respond to tax
As Certain as Debt and Taxes: Estimating the Tax Sensitivity of Leverage from State Tax Changes
If I can recall papers that estimate the costs of tax avoidance and excess burden of taxation I'll add them as well. Suggestions welcome.