Your interpretation of scripture does not allow for a Democratic Republic.
On the contrary. There is nothing about God's "job description" for Government in Romans 13, as a Punisher of Civil Evils, which prevents people from freely electing Magistrates to execute those Punishments.
All that "my interpretation" of Scripture (which is simply reading Romans 13 for what it says, about the Duties of Government -- and neither adding to it nor subtracting from it) would prevent is the notion of a majority of the populace "democratically" voting to help themselves to the bank accounts of the rest of the citizenry, for whatever "good" social purposes they decide entitles them to the forced confiscation of Other People's Money.
Both God and Thomas Jefferson (hardly an opponent of democratic republics) argue against this sort of "democracy".
"To compel a man to furnish contributions of money for the propagation of opinions which he disbelieves and abhors, is sinful and tyrannical." -- Thomas Jefferson
Ergo, mandatory, tax-funded Government Schooling is intrinsically evil.
Its very existence violates and profanes the 8th Commandment.