Another important point is that the relation between children, their parents and the society they live in would be changed in ways that are hard to predict.
See, the current assumption (or rather, the assumption that socially still stands but that is already shaken by the current lifespan augmentation) is that once a child is an adult, it won't be long before they will eventually see their parents either die (before modern medicine) or retire (the current paradigm), and have to replace them.
They will get hired fast, to get enough experience with their notional parents while those are still in the workforce, and then quickly be needed in a full-time, important gig.
It's also worth mentioning that the society, right now, is built on the idea that full-time stable jobs are widely available, on one hand, and a strict necessity for anyone to reach any kind of reasonable level of material comfort, social adjustment and general happiness. When not the only way to get basic human dignity.
That assumption is old as balls, and it's hard to see it surviving the current state of technology and medicine, let alone what's about to come.
So what will probably happen is that we'l keep telling people that working 40 hours a week in a job you had for the last, like, 5 years, is a basic necessity, yet that it's nearly impossible to get 'em, because old people are a) living forever b) holding on to those jobs because they're a strict requirement c) creating machines that do other people's 40hrs/week jobs.
So yeah, now that stable, full-time work has been overloaded with all that junk, the conditions that make this paradigm possible have to be saved whenever they're menaced. Sometimes I wonder whether I'm the only one here who thinks that the point of working is to make the world around me a better place, rather than a way to reach some kind of social status and incidentally keeping a relatively helpful system up and running.
With those prospects of limitless healthly lifespans, those limits would look like either
- capping the timespan people are allowed to work, so that they can't hog those precious, limited 40hrs/week stable jobs that young folks need to get some kind of implicit economic citizenship
- creating demand for those, by doing the old sorta-Keynesian thing and just creating jobs. This has worked great in the past, 'cause those jobs looked like building the Golden Gate, the Hoover dam, nailing down the basics of nuclear physics, getting jet engines to work, and then sending people on the freaking moon. But now it looks more like working as under-trained wannabe-SWAT police teams raiding teen's bedrooms for small-time weed deals, building the like five thousandth M1-A1 the USArmy doesn't need, and stuff like that.
My ideal, which I can't even seriously hold as I watch how most governments deal with their respective economic crises, is to strip that socioeconomic status away from stable employment.
I picture guaranteed basic income as the very first economic stepping stone of that project. See, I would gladly accept a basic living wage to stay home, cook for my family, take care of the house, and whatever, while dedicating exactly all, and not one second more, of my daily intellectually productive work timespan to something relevant, I don't know what. I think that, all things considered, I'd be more productive at my programming job working 3 hours per day than my current 8-ish.
But this is an socioeconomic rant I need to refine and turn into a set of attainable political measures, and then get off my butt and militate for them.