Taxation is not enough to pay back the entire public or private debt since all the new money which is injected into the economy enters via the banking system as loans or via government bonds (also backed by debt at a 1 to 1 ratio); so no amount of taxation against those dollars is sufficient to cover the debt which was created as a consequence of injecting those dollars into the economy in the first place... Unless the tax rate was 100% - But that would be impossible for other very obvious reasons.

The only real purposes of taxation are to force people to keep using the fiat currency as a means of payment (maintain currency monopoly) and also to maintain scarcity of the currency as this helps to keep inflation under control (at least for consumables). But it doesn't actually prevent inflation in absolute terms because the government usually ends up spending more than it collects in taxes anyway (take loans from the Fed by creating new bonds); they mostly care about having inflation lower or proportional to other countries, not about preventing inflation.

The only way to pay off the debt would be to change the mechanism via which money enters the economy so that it is no longer tied to a debt as it does so. But then the question would be who should receive all that new debt-free money? Probably it will be big corrupt megacorporations via insanely large government contracts.