We can look at what NASA did after the Columbia disaster; namely, redesign the external tank, employ stricter quality control of the foam across the board, better monitoring of the heat shield integrity, and adding contingencies for being stuck in space with a damaged shuttle.

- They replaced the specific foam insulation that struck Columbia with external heaters, and redesigned other areas where foam was necessary to ensure greater structural stability + minimize damage to the shuttle in case of breakage. They also began more thorough inspection of any heat shield panels that would be reused between missions

- They added various cameras, both on the shuttle and on the ground, to monitor the heat shield throughout launch, plus accelerometers and temperature sensors. Also, the heat shield was checked manually on every mission once in orbit for damage, both with an extension to the Canadarm, and with ISS cameras when possible (a funky maneuver [0] where they would do a backflip to flash the shuttle's belly at the ISS for it to take high res pictures)

- Every mission from then on had a backup plan in case the shuttle wasn't in a state to return to Earth (this wasn't really the case before then, which is kinda wild). Another shuttle was always ready to launch, with a new configuration of seats to allow for sufficient crew space

- They sent up equipment and materials for repairs in space with every launch, though admittedly the usefulness of that was dubious and the repair kits were never used

Perhaps 'eliminate' was too strong a word, but there's no reason these precautions couldn't or shouldn't have been taken before it resulted in deaths and the loss of a spacecraft. (well, other than the aforementioned funding/politics/organizational failure)

[0] https://en.wikipedia.org/wiki/Rendezvous_pitch_maneuver

>Every mission from then on had a backup plan in case the shuttle wasn't in a state to return to Earth (this wasn't really the case before then, which is kinda wild). Another shuttle was always ready to launch, with a new configuration of seats to allow for sufficient crew space

Actually the backup plan almost every time was to just stay on the ISS until another Shuttle could be prepared. They only had another Shuttle on standby a couple times, during missions where they weren’t going to the ISS.

>They sent up equipment and materials for repairs in space with every launch, though admittedly the usefulness of that was dubious and the repair kits were never used

Yeah it wasn’t even useful for a situation like Columbia. It didn’t lose a few tiles or something, it had a giant hole punched into its wing.

There’s no fixing that in space. So I personally think they focused on situations they could theoretically fix, even though those situations weren’t what happened to Columbia.

Worth mentioning, this is all particularly fresh in my mind because of a recently released video by the excellent Classic Aerospace History channel on YT, "A Brief History of the Space Shuttle". It's two hours long and provides a reasonably detailed overview of the program, would recommend if you're into that sort of thing: https://www.youtube.com/watch?v=WtmOVxcga-Y