I think the answer to the question you posed in the title is "both." Battery life imposes major constraints on what designers of mobile products can do vs. what they might wish to do, but UIs also keep evolving. As long as some specialization of functions exists -- e-book readers vs. smartphones vs. tablets vs. personal navigation devices, etc. -- then there will not be a one-size-fits-all UI.
It has been observed that much of the success of the new devices has been in part due to migration to low power design and advances in battery technology which enables the consumers long enjoyment/utilization times between charging. But it is also true that there has been an overload on the features which impacts the power envelope and many OEMs are grappling with this issue for quite some time. The user experience per se does not depend on battery capacity but it makes a major difference as most of user interaction is audio-visual these days.
So yes, the OEMs would like to have uninterrupted power in the same/smaller package and eventually you hit a roof.
The idea that products today are being developed to address any number of tasks in our lives... also suggests that the market may be headed towards a "limiting factor" based on batteries and/or the unsure interface issue(s) that are cropping up everywhere.
The classic current example is one that Apple has had to wrestle with, namely the design of the iPhone4 as a result of critical battery drainage issues in both the iPhone 3G and 3Gs. Would the design of the iPhone have changed if battery life was not an issue?
The Other Tesla David Blaza5 comments I find myself going to Kickstarter and Indiegogo on a regular basis these days because they have become real innovation marketplaces. As far as I'm concerned, this is where a lot of cool ...