Then what is? What stops BTC from being a real safe haven?

Of course, there are many different factors that are not helping either: small market size, low liquidity, immature regulatory environment, but still, at the end of the day, we will finish at volatility because all mentioned factors only fuel it even more.

In my opinion, such high leverage on small markets with low liquidity is like asking for disaster, which almost happened on the 12th of March, when Bitfinex has "server problems", which stopped BTC price from falling to 0. Whales, or large individual investors, in such a small market could and for sure are hunting for liquidity, causing all these sharp spikes and selloffs. Of course, such fast price fluctuation are responsible for many liquidations on leveraged trades, as we have witnessed already, so many times during the last two years.

Of course, all these problems don't help BTC to be a safe haven, but still, I personally think that volatility caused by high leveraged trades on the small BTC market is the key here.

Cryptocurrency market capitalization is actually: $216 billion when global stock market capitalization in 2019 was $90 trillion and in this year only gained 17 Trillion in value, when crypto market lost during the last few years almost 600 Billion. https://www.cnbc.com/2019/12/24/global-stock-markets-gained-17-trillion-in-value-in-2019.html