The potential is very big in the field of transactions, basically the Blockchain will change the way of managing transactions (more efficient, faster, more secure and much cheaper!).. Today banks manage all transactions centrally but the disadvantage of a centralized system is that it requires heavy infrastructure and processes, controls at all levels so a big cost to maintain.

Now imagine that we reverse the model and that all these process of validation and storage of transactions are done automatically by the network itself. In the case of a payment, you'll initiate the transaction (via any channel such as payment card, web, smartphone) and at the time of the issuance of the payment request, all members of the payment network (we can imagine individuals, businesses, shops etc. through their devices or their representatives or third parties in a Cloud) will be responsible for verifying your transaction with the same controls as today, automated in the Blockchain algorithm... When your payment gets validated by consensus in the network, it will be added as a new block in this Blockchain from which each node in the network would receive a copy of the complete update.
The role of the banks will no longer be to process the transaction by authorizing, validating it... and registering it in a database, it will be to develop and maintain a secure Blockchain algorithm that allows the whole network to operate over the whole transaction chain. That's why the potential is huge for banks.

We have a saying, "If you can't beat them, join them!". Lol. Kidding aside, blokchain projects are really helpful. The banks and other institutions saw the greatness of blockchain. They wanted to adapt it so that it will make their transactions faster and cheaper. Aside from that, it is really very convenient to use. Blockchain has a great potential in the future.

We always have to be smart in our daily doings and always been part of the good team is a key note for everybody, that is why with blockchain we say, we are safe and it will not be surprise to see organization building on such a platform. If bank could trust and use then is a plus. Blockchain all the way.

The technology blockchein really very well helps banks. Banks began using ripple crypto currency, which is based on blockchein technology. They replaced it with an outdated SWIFT-medod, whose help funds were transferred. If earlier, using this method, the confirmation of the transfer had to be expected for several banking days, then when using the ripple coin this became possible in just a few seconds.

The banks did not initially see bitcoin and blockchain technology as competitors..Later, they saw that the technology was spreading rapidly and chose to use it..Because this technology is both fast and cost-effective.

These articles are discussing the benefits of trasferring money abroad. A swift transaction usually takes about one working day to go through, because bank workers are doing it manually. Cryptos don't have any borders, so transactions even with such a slow coin as btc take for now a couple of hours or even less on priority payment (which is stiil a lot cheaper than the one for transferring solid amounts of money).  Not only this means speed increase, but some mediators can be remoed as well. There's another important improvement for financial systems that comes with blockchain. The data cannot be faked, so a lot of problems with coding the information in the most efficient way is out of the question.

Not only it has been talked a lot of times already that some of us may start to get an overdose with it. But your question is answered in the articles links you posted. So are you telling us you didn't bother to read the articles but was just interested to make a post about something debated thousand of time here?

Maybe it looks different from the traditional way of banking, but what it provides is bigger than ever. It provides an efficient way of functioning which we cannot expect with any of the other services. Now the adoption from banking will make their services cost effective and more effective.

I believe, the reasons are pretty obvious even for such conformist organizations as banks: they have started seeing their apparent benefits.
For instance, the transaction costs even for large amounts are meager as compared to the standard banking rates. The security and reliability of the blockchain is like a dream come true for the banks, so no wonder they are willing to adopt it.