It feels like if we just made these big companies pay what they should in taxes we'd be able to take some big steps towards health care, better schools, improving our crumbling infrastructure...
I disagree. Corporate taxes are a drag on the economy, and maximizing economic performance is probably the single most effective thing we can do to improve quality of life for everyone long term.
Actually, according to the IRS themselves in their yearly report to congress, they yet again have not been given the resources to go after big companies or rich individuals who are clearly skirting tax laws (and which will inevitably cause a serious court case because fuck you for trying to collect taxes from anyone with a lawyer) so they are basically relegated to sending mean letters to average and poor people for a few hundred dollars here and there, and they STILL collect more money than they are given in funding.
The IRS has been begging for the resources to go after big baddies for decades, but the Feds have been gun-shy at going after any large company since Enron.
As an example, here's self-reported life satisfaction vs GDP per capita: https://substackcdn.com/image/fetch/f_auto,q_auto:good,fl_pr.... Similar graphs exist for life expectancy, years of education, calorie consumption, literacy rates, and so on.
If we want to increase government revenues we should focus on efficient taxes that minimize economic disruption.