When will we reach the state of more of less stable cryptocurrencies or it is in their nature and will never end?
I think it will continue to be volatile.
However, if one or two cryptos come to be what all other currencies are measured against, much like USD, Euro, Yen, and Yuan are today, then those crytpos will APPEAR stable as all others will be measured against them
Money is a strange commodity. It has no direct use, which is what makes it useful, but that also tends to make it unstable.
Fiat currencies are not actually stable, but they're the benchmark. If you look at the history of the US Dollar, for instance, it's current value is 0.0151693276195533 of it's originally defined value of 1/20th of an ounce of gold.