Removing the human need to sleep will undoubtedly happen at some point in the decades ahead of us. The potential economic benefits are vast, and so as soon as it becomes remotely plausible we will see tremendous investment in realizing whatever biotechnology ultimately makes it feasible. You might look at the present large and ongoing investment into developing sleep suppressant drugs that are free from significant side effects as a small foretaste of what is to come.
A life without sleep would be a life effectively made 30% longer. There's a thought for the day - not all methods that might be experienced as life extension involve your body being alive for more calendar years. For example, one of the advantages of the very long term goal of incrementally replacing brain cells with nanomachinery is that it opens up the possibility of increasing your "clock speed": of thinking faster and experiencing more time per second than a present day human could. By that point, of course, we would hope that much of the challenge of aging has long been solved.
Imagine that human culture has never experienced sleep, but suddenly must experience it to survive. Would they be apprehensive about experiencing it for the first time? Of course!
Just picture... this total suspension of consciousness, experienced for the very first time in human history. The notion would totally blow our minds. It would be completely shocking. We might even make up stories about dying and being replaced by an identical clone being, or trying to console ourselves that at least we will have a successor on the following day to carry out our desires.
Contrary to popular belief, there is no particular reason to assume that humans who "survive" events like freezing or vitrification would be any different from humans that "survive" sleep or anesthesia. The definition of consciousness we care about is the lifelong continuity of experiences created by memories.
Our memories are encoded in the fine structure and connections of our brains, and for so long as that structure is preserved then we continue to exist as a person - whether or not our brains are currently in operation. The essence of cryonics is to preserve that structure after the point at which our bodies and modern medicine are no longer up to the task. The molecular nanotechnologies and biotechnologies of the future will be capable of restoring a preserved brain to active life: it's just a matter of organization and waiting, which in and of itself is no small challenge, but not an insurmountable one either.