A few random thoughts ...
Income and corporate taxes are just part of the tax system. Americans pay a wide variety of taxes. These include sales, property, payroll, state and Federal income and corporate taxes, and more. Many of these taxes are regressive, meaning that lower income families pay a higher percentage of their income for these taxes. Sales taxes and payroll taxes are example of regressive taxes.
There are some "hidden" taxes, such as resource extraction taxes (severance tax imposed on the removal of non-renewable natural resources) and state lotteries. The severance tax is borne primarily by consumers, and is therefore regressive - and lotteries are also regressive.
The main non-regressive taxes are income and corporate taxes. Higher income families generally pay a higher percentage of their income for these taxes. So when there is a discussion of reducing corporate and income taxes - and "broadening the base" for income taxes - this makes the entire tax system more regressive.
To make the system more progressive (where higher income families pay a higher percentage of their income in taxes), the discussion would be about decreasing regressive taxes (like the payroll tax), or increasing income and corporate taxes.
Why change the tax code? There could be many reasons to change the code: to make it simpler, to encourage certain activities (homeownership, investment, education, etc.), or to remove existing tax preferences, to spur growth, to reduce the deficit, to change the balance of who pays taxes.
As an example, to spur growth we could look for ways to lower income and wealth inequality (this is slowing growth in the US), and also ways to put more money in the hands of low to middle income families (people who tend to spend additional money). Examples of policies to spur growth in the short term would be reducing the payroll tax, and for growth in the longer term, increase the estate tax (and make it unavoidable).
What about the business cycle? If we look at the business cycle and the deficit, economic theory suggests that the government should increase the deficit during economic downturns, and work down the deficit during expansions. The economy is currently in the mid-to-late stage of a recovery, so decreasing the deficit makes sense now.
Conclusion: Right now it might make sense to reduce the payroll tax, increase income taxes - especially the estate tax (and make it unavoidable) - and reduce the deficit. Basically the opposite of the current proposal that reduces the burden on high income earners, offset by more debt and increasing the burden on low-to-middle income families.