But then even bitcoin is pegged to a fiat, to make it usable.
I am trying to understand is there a better solution to this pegging to government-controlled fiat currencies.

Bitcoin is
not pegged to any other currency, fiat, government, or otherwise.
"Pegged" means that the values are kept in sync. A USD stablecoin is "pegged" to the value of USD. Bitcoin is not "pegged" to anything.
The price being quoted in a particular currency does not mean that it is "pegged" to that currency.
You can buy bitcoins with any currency. You can state its price in any currency. Its value changes with respect to those currencies, therefore it not pegged.