Well it has potential to do that but the track record isn't that convincing. For example whole crypto has been very reactive to world events and especially stock prices.
Also Bitcoin is still under heavy fire because of POW and more the price grows, more heat it will get especially now when whole europe is trying to save electricity it will be seen as someting to get rid of by ton of politicians. And intensity of regulations for trading cryptos is just going to increase to the point that original pseudonymous cryptopunk idea is far gone. There will be way more blacklisted accounts and if tracking doesn't work they just ban fiat pairs.
All this pressure is definitely affecting trust on bitcoin as a safe heaven of any kind. Then again, there are different kind of voices in people making laws, so we might see some rebellion against regulators, but i very much doubt that as we are slowly losing the physical cash too.