No, bitcoin may be scarce but it's a cryptocurrency and those can be made by a computer program.
Think of bitcoin like Gold #1. When the supply of Gold #1 is exhausted or the price is too high, the market won't switch to platinum or silver. The market will switch to mining Gold #2, which is simply the next stable cryptocurrency of choice.
As the FTX scandal showed, the demand for cryptocurrencies is for their use in money laundering, bribery, tax evasion, and circumventing campaign finance laws, not their scarcity.
That is simply not true. At all.