To explain more, for e.g., we hear that the USD was backed by the convertibility of this currency to precious metals until 1971. Now, what are altcoins backed by such as Ethereum or Litecoin?
fiat is centralized that is why it
has to be backed by something, otherwise it becomes worthless. cryptocurrencies that are decentralized don't need that so you shouldn't compare them to each other.
as for ETH and LTC, their values are only based on purely hype and the pumps and dumps they get since although they may have some small utilities that they offer but it is not meaningful enough to give them any meaningful value.
Are mathematical calculations performed by ASIC miners any useful in the real world?
your question is unclear. ASIC is a general term referred to "Application-specific integrated circuit" and these machines do a lot of different things depending on what they are designed to do. you can read this for more information:
https://en.wikipedia.org/wiki/Application-specific_integrated_circuit