Other terms used to describe a "black box" include Flight Data Recorder (FDR), Cockpit Voice Recorder (CVR), MADS (Modular Auxiliary Data System), and OEX (Orbiter EXperiments) recorder. Other spacecraft have used them. What about Starship?
It should be noted that Elon mentioned during a Starbase Tour video that cameras inside the tanks would be able to observe excessive heating due to a failure of the thermal protection system tile during reentry...
[Elon] So, hopefully, we at least find out where the crack in the armor is...
[Tim] How will you know? What if something just goes... What if the first orbital attempt just goes totally, it doesn't even make it in for reentry and it's just a million pieces of the bottom of the ocean? How will you know where it failed?
[Elon] We have temperature sensors. (long pause) Probably need some thermal images inside the tanks. So, just like IR cameras.
[Tim] So you can see if a certain section's getting real hot.
[Elon] Yeah, IR cameras on the inside will show you what the backside temperature is.
[Tim] Yeah, yeah, it'll let you know if a leak propagated.
[Elon] It's only gonna pop if the backside temperature... Frankly, I'm not sure. In fact, I take that back. If you just have a camera-camera ... if something's glowing white-hot, okay, that's bad. That's the bad part, right there. So, you don't even need a thermal image, frankly. The steel will glow white-hot before it melts.
[Tim] Right, right, right. You'll know.
[Elon] You'll know. It's not subtle.
This conversation suggests to me that a black box of some kind would have been needed.