Leaving aside the cognitive dissonnance of providing federal funds to ensure that kids can go to any school, no matter how terrible it is, while at the same time arguing that the federal government should in no way take even the most marginal steps to provide health care for those children, school choice is a terrible idea.
A few quick facts (sorry to ruin the party!) Public education is largely a state-- and actually mostly a local-- function of government, but states and local governments (which mostly fund public schools via property taxes, a tax that [like all taxes but particularly this one] hurts middle-class and poor people most) get lots of funding from the federal government.
Or they did. Over the last five years, federal spending on public education dropped nearly twice as fast as federal spending overall did. This year, the federal government will spent about $42,000,000,000 on public education.
The modern voucher programs began with Milwaukee, in 1990, which created the first voucher system. At the time, 60% of Milwaukee students were dropping out before graduation and the average grade for students was a D+.
26 years later, one result has been that the Milwaukee Public School system has a higher-than-average load of students with special needs, and voucher students and non-choice students scored roughly equally. (That link, which touts that voucher students do better, ignores the actual statistics:
On the Badger/DLM exams, 27% of students in the Milwaukee voucher program were proficient or above in English language arts, compared with 25.6% of all MPS students and 20.5% of those considered economically disadvantaged. Sixteen percent of Milwaukee voucher students scored as proficient or higher in math, compared with 15.8% of all MPS students and 13% of those economically disadvantaged.
Yes, the voucher programs had a slight lead on the standardized test.) Results were better for voucher program students on the ACT college entrance exam.
Other results are mixed. A compilation of studies in 2011 found little difference in math abilities between voucher- and non-voucher similar students. Voucher students were slightly (4-7%) more likely to go on to and finish college.
One thing to remember is that education doesn't happen in a vacuum. While voucher advocates like to credit voucher programs for those advancements, one can't rule out the fact that students who switch from a public school to a private, voucher-paid school may have parents who are more engaged and more educated themselves, and thus be more inclined to do well academically. One of the key factors that determines if a student goes to college and does well there is whether that student had at least one parent who went to college. Another, as you'd guess, is income.
Among the factors that play into that lack of success, that last report noted:
If these obstacles were not enough, first-generation students typically have less well developed time management and other personal skills, less family and social support for attending college, less knowledge about higher education, and less experience navigating bureaucratic institutions.
Meanwhile, 81% of public school (non-voucher) students nationally graduate from high school on time, and 86% of those students have a college degree by age 26. Overall, educational achievements have been rising even though only 0.5% of all students are currently voucher students.
Competition among institutions can, indeed, make them better. (Ironically, many devout social conservatives believe in, if not Darwin, social Darwinism.) But there is no social issue that can be boiled down to black-and-white, single option methods.
I have long been in favor of 'public option' provision of social necessities: public schools, public health care, and the like. This works best when the government provides a robust public option at affordable rates, and then makes it possible for people to opt for that, or a private option, depending on their whim.
Here's an analogy: like education, and health care, delivery of information and goods is a public necessity. The United States created a "Post Office" in 1775. The USPS was funded directly by the government until 1971; now its funding comes from receipts for its goods and services, but it relies too on tax exemptions and low-interest loans from the government. (Some of the problem, if it is a problem, comes from Congress' requirement that the USPS pre-fund its retirement, a law Congress passed in 2006.) It is, though, for the most part, privately funded now.
The existence of the post office, with its government support, has not stopped the development of fax machines, emails, private courier services, and the like. In 2015, the parcel delivery industry had revenues of $150,000,000,000.
People can use the post office, trusting that it will get the job done: packages will get there, safely. People can opt for the slightly-more expensive private services, which have to be good enough to compete. The USPS uniformly has a lower cost for most immediate shipping, but UPS and Fed Ex and others make up by having (for example) higher weight limits.
School choice vouchers are the equivalent of the government taking away all benefits for post offices, and using that money to give you a coupon to select a shipper from anyone you want; but if they did that, the USPS would still have (for example) the congressional mandates that it pre-fund all retirement (private companies don't have to) and that it deliver everywhere (private companies don't have to). So a Mail Voucher system would handicap the USPS while, technically, saving no money (since the government would be handing it out in vouchers.)
One possible outcome of such a move would be to essentially end, or at least set on a path to destruction, the public school system. But why would Trump and Billionaire Betsy want to move the state and federal funding from public schools to private schools?
The last time a simple solution to a complex problem worked was when Alexander cut an ox-cart free from a post. That turned out well for him, right?