Yes as long as they wont going to accept by governments they will stay volatile like today.

So, it will never change according to you. Most governments will never allow themselves to lose power over the money because they know that as long as they control your wallet they control you.
When will we reach the state of more of less stable cryptocurrencies or it is in their nature and will never end?
Crypto market is only nine years. Current capitalization in the amount of 700m is nothing compared to the gold or US dollar market. When capitalization grows, volatility will decrease by itself. The decentralized market of the Earth's scale will be very difficult to swing.
The more money on the market the more money is needed to cause a move. Right now to significantly move the price on one of the big exchanges you need 3-4k BTC.
This means that you need 36 million USD to change the price by something like 500 USD, which is a very small move like 4%. Back in the day, in 2015 ($300 BTC) you needed just 16 million to cause a 50% swing.