I don't get something: if the point is to assure pensioners a pretty similar life quality to the one they have today, with shouldn't be that by 2050 it would be easy and cheap ? How does that go into the calculations , if att all ?
Effectively your arguing that productivity growth will effectively bail us out of our high levels of debt and pension obligations (which are another form of debt) and there are more than a few that have argued the same. The challenge is that productivity gains have been slowing. Computers and the internet are now fairly mature technologies and aren't driving the productivity gains we saw in the 80's and 90's. Also as…
For example, some claim that the reason we don't see Productivity growth across the econmy is that because people(across all age groups) take the money saved from sectors with growing productivity(say, manufactured goods) and use that in sectors with stagnant productivity , say restaurants, plays ,spas , etc.
As for the shift towards nursing care - yes, it is true today, but one could imagine(and some are building) all kinds of technologies that reduce that need and it's expense.For example, if there was a really affordable and good: custom meal delivery, transportation , telehealth and medical adherence , fall prevention, some arrangement that prevents loneliness, and some better medical treatments and tools to age related diseases , and many of today's drugs will be off-patent[1] - it's possible that elderly treatment cost, at today's quality levels would go down significantly.
[1]Of course ,new treatments should be too available to seniors, and that raises the question of ever growing health care costs ,which is a big issue itself.