Well, as I mentioned above, asymmetric encryption is notably weaker than symmetric encryption in certain respects, so you certainly wouldn’t want to use asymmetric as the default in an encrypted backup system. Maybe some individual users are willing to sacrifice some security for some convenience this way, but it shouldn’t be the default.
On the other hand, it’s also possible to use PGP for symmetric encryption, which might be what you’re referring to. I vaguely recall that this possibility was considered and discussed in the aforementioned thread and ultimately rejected because it did too much parsing on untrusted input, but this was many years ago.
This leads me to one of the most important reasons that the Qubes backup system is the way it is: authenticated encryption. Many encryption programs don’t allow their encrypted output to be properly authenticated. If you tried to use something that like for Qubes backups in dom0, it would be a major security risk, since attempting to restore a malicious backup file could compromise your entire system. Thankfully, the Qubes backup system was specifically designed to defend against this sort of threat, which is why it verifies the authenticity of all purported backup files before parsing them.
Designing a backup system is hard to get right. Encryption is even harder. Unless you are an expert, it is generally not a good idea to try to roll your own. Better to use the proven, time-tested tools developed by experts, especially when they’re already built-in, IMHO.