Why is there no POV video of the Philae lander landing? All I can find are animations made beforehand mixed with commentary and one or two stills.
According to this statement by the ESA,
Rosetta is presently sending signals to the ground stations at about 28 Kbps; Ignacio says that the spacecraft's own telemetry downlink uses about 1 or 2 Kbps of this, so the rest is being used to download science data from Rosetta and lander science and telemetry from the surface.
Given that you have 28 kbit/s for the total spacecraft data downlink, and assuming that the lander sends approximately the same amount of telemetry data as Rosetta, we are talking about approximately 25 kbit/s for science data (which I use here to mean data not related directly to the spacecraft itself or its operations, which may or may not be the same meaning as that used by the ESA).
25 kbit/s isn't a whole lot at all. If we assume that is the payload transmission rate, we are talking about roughly 3100 bytes per second. The text of this answer, not including the links or formatting, is about 3000 bytes.
Take for example this photo, taken during descent. The "high resolution" version posted on the web is 817 x 795 pixels, and it is in grayscale. If we assume one byte per pixel (8 bits shades of grey) and 50% compression (which is high for high-quality photographs, although by no means unattainable) that required downlinking about 320 kilobytes, taking about 104 seconds of payload downlink data capacity to downlink. And that's assuming that the native resolution of the imager wasn't higher and the image was later, on Earth, downsampled or cropped for posting on the web.
Even if the lander had sufficient buffer memory to be able to record even, say, one image per minute during the descent and landing, it would still have needed twice as much time to downlink the data to Earth, assuming no other measurements are transmitted during that time. Given that the landing and settling took several hours, and the downlink isn't usable all the time due to occlusion of the Rosetta spacecraft, that would have left us for several hours receiving much less scientific data than we could have, in order to have a video of the descent, most of which would probably have been rather uninteresting to everyone except the most devout followers of the project.
Probably wouldn't have been worth that tradeoff. I certainly wouldn't have made such a tradeoff.
And increasing the downlink speed isn't necessarily trivial; if increasing the downlink data transmission rate was easy, I can see no real reason why the team would have settled for 28 kbit/s.
The above assumes, too, that we are talking about 28 kbit/s usable after error correction is accounted for. I have no references to back that up, but I would expect error correction data to correspond to a significant fraction of the raw downlink data transmission rate. The last thing you want is to send a spacecraft several hundred million kilometers away and then not be able to receive the transmission because it's been garbled beyond the ability of the error correction to recover from.