It could be argued that one of the reasons why people are willing to put aside consideration of rejuvenation research, and the related prospects for therapies to turn back aging, is that most underestimate the burdens of age. They are young enough to not be personally impacted today, and the older people they know don't tend to be all that open about the challenges, the pain, the suffering. No-one wants to be the walking medical catalog in the conversation, but everyone gets to be just that at some point, when it can't be hidden away any more. From a stoic perspective, if being old isn't that bad, and then you die peacefully, then that isn't such a terrible situation to be in. I think many people have exactly this errant view - that being old isn't that bad from a physical and mental perspective. Yet it is, it is. It is just that older people tend to be reserved about their suffering, popular entertainment features fit and happy older folk, and most younger individuals only have to go through the process of brutal disillusionment once, with the decline of their parents. That still leaves much of a life span in which those illusions can be maintained.
The ill health of old age is a formidable sword of Damocles looming over us all, and when it falls down, it typically does not hit just us; the elderly are certainly the primary victims, but their family are collateral casualties. When people lose their health and independence to aging, their families have to go through the pain of seeing their loved ones becoming more and more fragile, sick, dependent, perhaps even demented. Adding insult to injury, the troubles caused by aging don't stop here, because a sick and dependent person needs looking after. Thus, the family of an elderly person needs to step in themselves to take care of their relative; if this is not possible, a nursing home is likely going to be the only option left.
Personally taking care of a sick elder is no joke. It requires patience, effort, and most of all, time. It's a real challenge, especially so for people who have young kids of their own to look after. Let's also not forget that it is emotionally very taxing. The nursing home option may partly solve the problem, because there, somebody else does the caring for you, but telling your elders that you can't take care of them any more isn't the best feeling in the world, for you or for them. This can be a rather costly solution, too and as much as every last penny spent to take care of a loved one is well spent, a typical family only has so many pennies, and just because they need them for grandpa, it doesn't mean they can conjure money out of thin air.
As things stand, when we're going to be old, our dear ones will be faced with the issues above; however, if a decent rejuvenation platform was in place by then, none of these issues would materialize, because we'd be healthy and independent in spite of our age. We would never be a burden on our dear ones, and the time we'd spend together would be quality time for us and for them. Luckily for me, I'm still very far from that stage of life when all your friends of a lifetime keep dying. I like to think that there would be more than one person grieving for my loss, and I believe that would actually be the case for most of us. If we exclude few, rare scenarios, your friends, and family would probably rather have you alive and well than inside a coffin. Thanks to rejuvenation, your spouse, your children, your grandchildren, and your friends may benefit from your presence, life experience, and persona for a much longer time. This would be a benefit for you as well, because you could live through your 80s, 90s, and who knows how much longer, without having to bury a dear friend a few times a year.