It's not just for paywall bypassing. Sometimes there are archive.today snapshots that aren't in the Wayback Machine (though I think your overall point about lawlessness still stands).
For example, there was some NASA debris that hit a guy's house in Florida and it was in the news. [1] Some news sites linked to a Twitter post he made with the images but he later deleted the post. [2]
The Wayback Machine has a ton of snapshots of the Twitter post but none of them render for me. [3]
But archive.today's snapshot works great. [4]
[1] https://www.bbc.com/news/articles/c9www02e49zo
[2] https://xcancel.com/Alejandro0tero/status/176872903149342722...
[3] https://web.archive.org/web/20240715000000*/https://twitter....
Archive.today has a different approach to the baseline archive technology (executing javascript at archival time and saving the DOM instead of saving and replaying server responses verbatim). Additionally, Archive.today employs a number of site specific mitigations which aren't visible to the end user. In some cases, for instance, they use accounts, but then retroactively modify the DOM to mask this mitigation. [0] While the exact strategy they use for Twitter isn't known to me, they are doing something by their own admission. [1]
[0] https://blog.archive.today/post/708008224368001024/why-isnt-... compounded with personal observation.
[1] https://blog.archive.today/post/708565142782246912/pretty-pl...