Indeed. This has been my gripe since first SpaceX booster landing attempts - I understand that "livestream from an IMAX camera" may be very low at the list of priorities for space missions, but... it shouldn't. Even if recovered after the fact, having a solid, high-quality footage from flight and orbit would make a huge impact on the publicity goals they're all explicitly trying to achieve. There's a shortage of good footage from space; at this point, a 4k/60FPS recording released in public domain would easily redefine how space scenes look in movies, TV and video games in the next decade[0].

I'm not saying it's an easy engineering problem, but at least for LEO, the recording side is a solved problems (we all carry more than good enough hardware in our pockets), and the major challenge would be about keeping the lense/viewport clear throughout the ascent, and dealing with vibrations.

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[0] - It already happened many times. The step shift of how black holes are portrayed after Interstellar folks did the math is the most obvious one to notice; more subtly recent productions seem to also take into account the asymmetry of the brightness, after the telescope photo of a black hole reached public awareness. But even earlier, there's e.g. been a change of how planets are shown - you see much less of the geographical atlas spheres with clear continent lines, and much more of low-angle, close-up shots that look suspiciously similar to the footage from the International Space Station.