Free market economics is renowned for its competition and the necessity of business to become evermore agile and adept in doing business because of that. However, the Federal Reserve has established a sort of horizontally and vertically integrated monopoly on money; it can "sell" (i.e., loan) any quality of money without any (domestic) threat of competition so long as (1) legal tender laws are enforced consistently and (2) it supplies the notes (be they FRN 1, FRN 2, FRN 3, etc.) itself.
The short answer is that the authorities probably won't try this strategy because of the low chances that the populace will end up putting much wealth in the FRNs.
The long answer is that financial repression alone, especially financial repression by law (e.g. legal monopoly) has rarely, if ever, been enough to support the modern monetary system in the West. Even under the last paper-money regime in China, when all power was concentrated in the emporer, there was virtually no contact with foreign countries, and using anything other than the state paper money was punishable by death, eventually the state saw fit to go to silver.
To my thinking, modern money has always survived by distributing its weight among all of the following major devices of support, and not any one alone. I think this distribution will be even more necessary in the future as trust in the elites continues to diminish and power will continue to shift from the US-Europe axis to the developing world.
Remember that the fundamental problem for mondern money is that the problematic incentives for the elites always end up creating more paper claims to wealth than real goods and services, and so the following support systems become necessary to keep the system alive:
1. Political repression- Acquiring colonies and making them hold paper sterling as reserves, by Britain.
- Working with China and oil-rich dictatorships to support the dollar in exchange, effectively, for safeguarding the regimes' power.
- Encouraging poor countries to issue too much money and debt so the dollar becomes trusted and hoarded by individuals.
- Problems for the elites: international inequality, social instability in poor countries, terrorism and war.
2. Financial repression by law or market manipulation- Banning of private gold ownership (US.)
- Legal caps on bank interest (US.)
- Capital controls (US and Europe under the Bretton Woods system.)
- Driving savings into bank assets by, effectively, taxpayer support for banks and loose bank regulation.
- Loose monetary policy.
- Suppression of gold and silver prices via derivative trading.
- Exporting economic instability and pain to developing countries via the "exorbitant privilgeg" process.
- Problems for the elites: market-developed evasion (e.g. money market funds and euro-dollars;) financial fragility (due to distortions of asset prices by policy) and instability; developing countries fighting back (Asian currency manipulation was a big part of the causes of the 2008 crisis.)
3. Acknowledgement of reality- Price inflation over the long term.
- Devaluation of the dollar against gold during the Great Depression.
- Allowing gold price to go to $300 and then $1200 per ounce under the fiat system.
- Dollar devaluation against Deutsch Mark, euro, yen and yuan in recent decades.
- Monetary/fiscal tightening (e.g. early 1980s US, present day European periphery.)
- Problems for the elites: exposure of the system's weakness to the public.
(Note that, often, a device is a combination of the above categories. E.g. Western equities and real estate are indirectly propped up by central bank policy (low interest) and enjoy long-term appreciation which reflects the weakness of paper money against "real" assets. These are excellent devices from the elites' point of view as they naturally divide the weight of the system among multiple pillars.)
In short, the survival of the system depends as much, if not more, on "soft power" as on "hard power." For example, the very reason that the world still trusts the dollar is that the US is perceived by many to have an open and free financial system. The reason Americans and foreigners get into dollars and Treasuries is that they know they can get out.
This is not to say that creditors hold much power over debtors, or rich over poor. The various repressions make clear the authorities' ability to punish savers of all types. But any redistribution of wealth to the poor, especially under a complex and disguised system such as this, tends to reflect power grabs by the elites. Genuine help to the under-privileged of the world, and especially allowing them room to help themselves, can really only come about when the economy acquires real wealth in a stable, sustainable and equal manner, and that can only happen when the world system is no longer destabilized by state-issued money.