And it would not be impossible to coordinate the return timings to match either.
Or even better, to have just one low-level packet shared among them all, with a mobile operator or backbone protocol that fans them out and in, analogous to multicast and IGMP but designed for push/keepalive systems.
There are no insurmountable technical obstacles. Just challenges.
There is negligible consequence for power consumption too, with a suitable API.
But rather than design for everyone, as we would have seen in the utopian days of the internet, it's much easier to run a single walled-garden service, and it fits with the "you must go through us for everything" model used by many of the device's other services.
But not on major mobile devices, at the moment.
In the banking world, it appears to be getting slightly more open. There are more independent feeds and open standards than there used to be. This is a mixed benefit as there are also more "middleman" sites that want to read your banking data to help you visualise it better, and some of them might not be doing it just for the benefit of the account holder.