Human Mail: This is what “steerage-class” transportation is. In the old days they’d freeze you down (Human Popsicle–style), and in the new days they put you into nanostasis, but either way, at the sophont shipping center they pack you into a body pod, stack them three by three by two into a powered (“reefer”) shipping container, and send the result off as freight to the sophont receiving center on your planet of destination, where they revive you. (Unless something goes wrong and you end up at the lost sophont office, but that hardly ever happens.)
In addition to being the favored transportation method of the poor and near-poor (because it’s obviously much cheaper to ship a corpsicle than something that needs life support), it’s also widely used for bulk personnel movements, like prisoner transfers, colonization ships, and troop transports.
Human Popsicle: Cryostasis used to be a standard way of storing people, and was taken advantage of for a variety of purposes, specifically including the Deep Star projects (subluminal interstellar colonization of the Thirteen Colonies, with ships full of frozen people), and, in the time after the prospect of fixing the dead was mooted but before the technology to do so was available, freezing something very close to everybody who died accidentally “for later”, in the Vaults of the Dead Awaiting. Hates the permadeath, they does. Some people, chrononauts, even used it electively for, to be closest to the spirit of the trope, deliberate one-way time travel into the future. See history while skipping the boring parts!
In the modern era, cryostasis is an archaic technology, mostly replaced with digital archiving for minds and the rather more high-tech and less damaging/risky nanostasis for organic bodies, but the effects and the purposes for doing it remain much the same.
Cryonics Failure: While not nearly as bad as some of the examples given under the trope – for example, with the exception of the ill-fated Valiár (Thirteen Colonies) mission, whose failure was the result of engine defects rather than cryonics problems, virtually all of the cryostatic colonists were revived safely on their arrival at their destination – cryostatis always posed some problems (due to cracking and ice crystallization damaging cells), resulting in difficult and medically intensive revival processes and often-severe “revivication sickness”.
Which is why, once it was invented, it was very quickly replaced by the more advanced nanostasis process, which replaces freezing by the emplacement of a “vitrification scaffold” which preserves the body over long durations, does not require extreme cold for maintenance, and is optimized for the stop and restart parts of the process. Much more effective, especially when you can store the mind outside the body just in case.
Cold Sleep Cold Future: Averted. The thing about widespread immortality is that even the first-generation cryonauts, the people frozen en masse after fatal accidents from about, oh, a week or two after someone figured out this whole thing might be possible, walked out of the revival vat and into the embrace of old friends. Future-shocked as hell, I grant you, but not exactly “cold future”.