I believe the AddKeysToAgent option (see `man ssh_config`) does what's being asked for here. As usual, it can be enabled either in the ssh system/user config file or via `-o AddKeysToAgent=yes` on the command line.
This feature was added in OpenSSH 7.2, which appears to be older than what's found in any currently-supported Debian version. So I imagine this bug can be closed. -- "In the beginning the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move." -Douglas Adams
