A lot of these "loopholes" are actually progressive policies meant to grow the middle class through the tax code. For example: the first-time home-buyers tax credit promotes housing, tax rebates for children allows parents to raise children, or tax deductions for repaying college loans makes education more affordable. There might be better ways to implement these same policies without using the tax code, but no one is proposing doing so at the moment. If you just cut these tax "loopholes", then it is the middle class that ends up paying the price.
Even the idea of capping deductions to $25,000 that prima-facie appears progressive, may actually not be. One of yhe biggest tax deductions that would be curtailed is the one for charitable donations. The beneficiaries of charitable donations (aka the poor and sick) then end up being the ones bearing the brunt of such a policy.
"Lower the rate, broaden the base" often means cutting benefits for the working class to cut taxes for the rich. Not always, but often.
There is one major exception: Social Security payroll taxes. The Social Security Trust Fund - meant to pay for retirement - is maintained by a 6.2 percent tax on employees' wages with a matching 6.2 percent paid by the employer on the first $110,000 on income. A person who earns $110,000 therefore pays the same amount in payroll taxes as a person who earns $1.1 million dollars.
If the $110,000 cap was lifted to cover all income, then the payroll tax rates could be lowered in response.
That's a progressive "Lower the rate, broaden the base."