My understanding is that the EU PSD2 regulation indeed is supposed to make banks adhere to a standardised API. That being said, I wouldn't expect a super easy to use REST api with documentation powered by readme.io.
If you read the legislation (?) you will see that they are actually very vague in how the banks will provide access. I think it is already a great success that they (fingers crossed) will manage to force the banks to provide access to the data in any form and gave them little wiggle room for justifications to get out of it.
There are however some inititives for open API standards that might be accepted by a majority of the banks.
No, they're just told to implement the technical means so that the user can decide what to do with their personal data. This probably means some kind of API but any bank is allowed to implement them in any way they like.
That's obviously and opportunity for Teller, Figo.io and other players, they can perform legit aggregation just swapping out their scraping for bona fide API access.
But the situation is more complex... even banks can become aggregators for other banks if their customers want... These are interesting times.
There are however some inititives for open API standards that might be accepted by a majority of the banks.