People would still be using Bitcoin just not on chain.
When the dollar was backed by gold it worked perfectly well and the country experienced its greatest growth.
The difference is - the government enforced a
single currency. In a decentralized system, nobody will.
This severely hinders the utility: by adding a mental effort to decide which off-chain to use and by introducing friction at borders.
You will get the same mess we have with altcoins now, only it will also be even less clear what is securing each individual off-chain.
With all the alts out there Bitcoin still commands >99% of the market share. The free market and network effect have already essentially recognized a single cryptocurrency.
Also in the past the situation you worry about already existed. US Dollars, British Pounds, French Francs and other currencies were all backed by different weights of gold. Essentially these currencies can be thought of as off-chains. Converting one to another was trivial.