Having done both professional photography as well as professional videography, I have a lot of experience in both of these areas. They have many similarities, but also many differences.
The technical capabilities of the tools have already converged to some level and will continue to do so. DSLRs are one of the more popular choices for shooting video now due to the low cost and high quality as well as interchangeable optics. Major TV shows have actually been shot on DSLRs. (The last two episodes of House were shot on the Canon 5D Mark iii for example.)
That said, the fields themselves are no closer to converging than they have ever been. From the perspective of a photographer, capturing 30 images in a second is largely noise. There are some environments where it is helpful, such as sports, but in general a photographer is looking for one perfect image while controlling as many variables of that moment as possible. A videographer on the other hand is controlling the behavior of their camera to capture a scene as it unfolds.
The language of the mediums, while similar in terms of composition and many techniques, such as lighting, is completely different when it comes to how emotion and story is communicated. Photography cares about capturing the essence of a moment in crystal clarity while video is concerned with capturing the beauty of motion and telling the story through flow.
Similarly, on a technical level, the quality of image we can capture at slower frame rates will be higher for quite some time still (until we are regularly hitting the diffraction limit for practical sensor sizes). We will get burst capabilities that rival film much sooner, but they will be to large buffers that fill rapidly.
Just at the 35mm format, we need video to be in the upper 20s or low 30s of megapixels before we hit the diffraction limit reliably. Until that point, the most quality for a photographer will come from shooting the moment rather than just capturing all moments. Even when we can capture all moments, sorting out the perfect moment from among all the images would be more painstaking than simply capturing the one moment that is needed.
Additionally, trying to capture all moments well detracts from how well you can look for and capture that one perfect moment. Photography requires focus on the moment while video requires focus on the whole time of the shot. They are different mindsets with different technical goals and requirements that require a different use even when using the same tools.