How does that solve the “unelected bureaucrat” problem? You still need bureaucrats to run a civil service, the appointed positions in U.S. institutions are mostly just figureheads, they’re not handling the day-to-day work of keeping a bureaucracy functioning.
Unless you’re suggesting that every bureaucrat role should be an appointment, and part of X years elections, is having people with appointment powers turning up with a list of 300,000-3,000,000 people to fill every bureaucratic role, and somehow the general public are going to scrutinise that in some meaningful manner.
All of that is of course ignoring the problem that comes with throwing away all of your bureaucracies institutional knowledge every X number of years. Do you really want the issuance of driving licences, fishing licenses, gun licenses, international visas, customs enforcement, immigration enforcement, to all grind to a holt every 3-5 years while the new folks figure out how stuff works? You would basically end up with a bureaucracy that fundamentally couldn’t achieve anything, and silly things like the rule-of-law would simply cease to exist in the U.S.
Why would anyone want to trade with, invest in, or ally with, a country that effectively lobotomises its government every few years, and has zero continuity of governance at even the most basic day-to-day items of modern life?