You’ve made a fatal assumption that what is “acceptable” content is immutable and can’t be retroactively changed so that safe content is now unsafe content.
They’ll never be free of the costs of content curation
That would likely require reviewing every item in the "time capsule", even in the parts that have passed moderation. Moderation is not perfect, and there is likely a risk that something crops up that has been missed, with more legal troubles down the line.
Hence they offer to make copies of whatever material you might consider worth keeping, before the shutdown. Likely you can copy the entire site and keep it as a time capsule, public or not.
Why not just leave a read only, static, site up and running so that these links and paste don’t disappear?
The moderation was the hard part, and for already moderated posts this cost has already been sunk.
Further: if the site is just a time capsule, the operating cost would be near zero.
Why not just leave the history in place?