Asymmetric encryption solves the problem of transmitting the password safely ("solve" is a rather optimistic word, maybe "delegates" is more appropriate); if you can safely transfer passwords from point to point, then using symmetric encryption is far easier.
Which is just a different problem, not necessarily an easier one, like you say.
Unless you're doing it wrong.
That's a very nice way to put it, I'm going to reuse that !
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Use GPG with the cipher AES256, without the --armour option, and with compression to encrypt your files during inter-host transfers. GPG
Encryption helps protect your files during inter-host file transfers (for example, when using the scp, bbftp, or ftp commands). We recommend GPG (Gnu Privacy Guard), an Open Source OpenPGP-compatible encryption system.
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scp shouldn't be in that list.
But for bulk data encrypting good symmetric (AES, CAST5, etc.) is both more secure and significantly faster.
This is how the same document can be encrypted for multiple recipients efficiently, without duplication all the data. First the document is encrypted with a symmetric key, which is then encrypted with the public key of each recipient. This information will be prepended to the actual encrypted document.
For details see: https://tools.ietf.org/html/rfc4880#section-2.1