Technically yes, definitely. It might have even been as Rosetta and Philae were designed, but was not considered a priority or was thought wasteful to already limited resources. For example, from technical standpoint, we frequently get downstream in the order of several megabits per second (Mb/s) from Mars orbiters (check for example the DSN Now tool, select a dish receiving data from some orbiter, and click in the right column + more details to see real time uplink and downlink info). Granted, Mars is currently 263 million kilometers away, not 510 million, but you also don't require that much of a bandwidth for some highly compressed standard quality of perhaps lower frame rate high definition videos transmitted in real time. We could certainly stuff some real time videos into downstreams of today's space-faring hardware. Or, alternatively, record them and transmit later at a slower data rate.
But there still wouldn't be much chance that it would be included, since it would hardly have any scientific or technical value beyond perhaps for public outreach purposes. And even if it was, it would have low priority among many other scientific instruments, all sharing same bandwidth. Scientifically speaking, there is no real justification for such bandwidth-starved real time videos on a celestial body where you get many times the scientific return on investment by using still cameras in multiple wavelengths whose data can be transmitted at the same cost to the spacecraft's bandwidth and power budgets. You can always stitch individual still frames for panoramas or display them in a time-lapse sequence for the animated effect, if that's really required. It might be nice to see them, so the general public can grasp easier what their governments have spent their hard-earned tax money on and why, but that's usually something for Public Affairs Officers (PAO) to justify once the mission budget has been approved, and those rarely (if ever) select scientific packages on spacecraft. Frankly, I think that's for the better and if public was asked what they'd want their scientist to do with fancy and expensive gadgets, it would probably yield fairly little science and have quickly-forgotten entertainment value.
It is however true that many space agencies lately put more effort into Education & Public Outreach (EPO, or sometimes E/PO), e.g. NASA does that through its Science Mission Directorate Education and Public Outreach (SMDEPO) community, among others, and such hardware is nowadays more frequently included on spacecraft, budget and other mission constraints permitting. One such example is JunoCam on JUNO spacecraft that will exclusively serve for POE purpose, and has otherwise little scientific significance to the mission.