When will we reach the state of more of less stable cryptocurrencies or it is in their nature and will never end?
Well that will take a very long time. The price will be stable when people are not getting big fractions of bitcoins and that will happen if the bitcoin is too high. For example you need to buy something for $1000 and you want to sell your btc for that. If the market value of BTC is $1,000,000 the price will not be affected so much if many people will sell $1000 value of btc.