Not correct. CCs are backed by the algorithms.
People have faith in the value of dollars (accepting a relatively small gradual deterioration over time due to inflation) because the supply of dollars can be controlled to prevent drastic swings in it's value. If the dollar starts dropping too fast, the supply can be reduced. If it goes up too fast, they can increase the supply of dollars. They can increase or decrease the speed the money flows through the economy by changing interest rates. So people have faith that the dollars they earn today will buy them a fairly certain amount of goods and service next month and next year. They have that faith because the US government/federal reserve system is in place to give them that security in the future value of the dollars they earn today.
In what way does "backed by algorithms" provide the same type of security that their bitcoins might not drop in half in purchasing power in two weeks?
You've got it all backwards. The dollar should not be manipulated in the ways you are suggesting. In particular the manipulation of rates distorts the credit market. Low rates were the direct cause of the 2000's bubble that led to the 2008 crash. The dollar value is supposed to change in response to the market supply and demand for those dollars. Manipulating it is political. Also there's no decent way to measure the value of a dollar,