Bitcoin can only become a safe haven if enough people truly believe that it is a safe haven
That's the hard truth. As much as we want, hope and try to see bitcoin to be, it would only be if majority of we the people see it to be or place it in a position of being that which we intend for it.
Fiat has got issues and those to whom authorises or backs it up but, bitcoin has got just the people. The whales, petty traders and holders combined. The more people get to buy in the idea, the more value it adds to itself.
It's been seen to serve as, you can't just issue new coins to serve an inflationary purpose or withdraw it from the system and the reverse results. It works solely based on how the masses perceives the dynamics that happens on the market. This makes it more better in serving public interest than we can say for fiat.