Just like gold, in fact, during a recession and bank failures Bitcoin may just perform very well, because it has limited quantity, it is decentralized, and it is relatively decorrelating from traditional financial markets.
The only reason bitcoin performed well everytime in economic crisis is because when world faces economic recession there is no other way to generate money so people start investing their money in stocks from which they get good profit and bitcoin is tax free so investors use it as secondary way of getting profit.
Will people invest in bitcoin and stocks or will they dump en masse to find safe havens like gold? If you spend time studying past economic crises, you will see that things happen the opposite of what you say. If you look at the economic recession that happened in 2008 or the recent mini-crises in 2022 caused by Ukraine and Russia, you can easily see that the entire stock and crypto markets have been severely sold off. So it would be wrong to say that bitcoin and stocks will do well during economic crises.
Also, bitcoin investors are not tax exempt, people who invest in bitcoin but do not pay taxes are tax evaders. There are only a few countries that are tax free but the rest even tax crypto investors very heavily.