Not necessarily. With photography having been digital for about a decade and home video for about half that, tech savvy families easily have several TBs of data that they would want to hold on to for the long haul. The prospect of being able to burn a complete copy of these things on a few discs and leave them at the grandparents or in a bank box seems very appealing, and only more so over the coming years.
And you're of course right about the cloud, especially in the US; I've got rock solid AT&T ADSL, but it's very A(symmetric) and has a 150 GiB monthly cap, so only my very most important stuff gets saved to rsync.net, which e.g. saved my email from the tornado.
Archival hard drives exist of course, but are at a cost disadvantage compared to tapes or optical media.
SSDs are way too young to depend upon, as far as I'm concerned. For that matter, if you really screw up and have to recover data from a drive, they're much more opaque than hard disks.