The adversary we are most worried about is a government agency in 2023 demanding a large Website turnover of all live data, backup data, and backup tapes. If a weakness in AES is found sometime before then, the agency can decipher secret data offline and in parallel, regardless of when it was uploaded to the server. In other words, the attack window for encrypted data stored on a server is infinite. If we're encouraging the upload of encrypted data to the server, the encryption has to be future proof, since server-side data is in practice never thrown away.
In the attack you mentioned, the secrecy of TLS via AES isn't at issue since there is nothing secret about our open-source libraries. If the integrity of TLS is broken (due to a real-time exploitable weakness of SHA1-HMAC or of the public key system used in session negotiation), then only those who upload data in the attack window are vulnerable. Those who downloaded and used TripleSec code before the discovery of the attack are not at risk, and of course those who use it after TLS is fixed are also OK.
Finally, I see no problems with older (i.e., 90s era) crypto constructions that haven't been broken. RSA from the 70s is still useful. The cipher cascade here is essentially a one-time pad, so predates Schneier and is better attributed to Shannon 1949: http://netlab.cs.ucla.edu/wiki/files/shannon1949.pdf