No I do not agree that banks would go extinct if they do not adapt cryptocurrencies in their payment system.

Remember, the greatest limitation of cryptocurrencies is on its nature- it solely exists on the internet. Without any device capable of storing your digital coins, this kind of payment method could not be implemented world-wide given that there are developing and underdeveloped countries that still struggle with other priorities.

For first-world countries, sure, banks may adopt cryptocurrencies on their system but fiat should and will always be king in the foreseeable future. Totally converting to a digitalize payment scheme would only benefit the rich and prejudice the poor due to the lack of any accessibility on the latter.