The engineers never "saw that the leading edge was damaged," and "they" (who?) never knew "they were going to die on reentry".
NASA could see from the launch films that there had been a foam strike on ascent. Their belief (not actually tested) was that such a foam strike wouldn't do anything more than cosmetic damage. It was deemed an "acceptable flight risk".
After the accident, they set up an experiment where they fired frozen foam pieces from a cannon at shuttle wing leading edges -- and blew big holes in the reinforced carbon-carbon that was the leading edge thermal protection.
Then they knew.
In retrospect, don't launch people on solid rockets (Challenger) and don't launch them on a spacecraft strapped to the side of a fuel tank, unless you're very sure (and have demonstrated by experiment) that that tank can't shed pieces that can damage the spacecraft.
NASA is still proudly violating that first rule (SpaceX certainly isn't!), BTW.
CONGRESS mandated that the new moon program shall use repurposed STS technology, including the RS-25 engines and the solid rockets. This is not what engineers at NASA wanted to do ... they wanted to build on lessons learned and designs perfected from the Apollo/SaturnV program. This is what CONGRESS shoved down their throats.
Meanwhile, SpaceX is doing what NASA pays them to do.
You are correct, it was on a later mission they had the camera that saw some tiles missing, not the Columbia. They suspected there could be damage, the DOD was willing to photo the wing with a satellite but it was not done.
*sigh* This getting old sh*t is for the birds when your memory starts playing tricks on you....