I'm unsure "having to" is quite the right phrase. "Being forced to by an uncaring society that would prefer to keep younger folk on the dole whilst bullying the older generation who have done their bit to keep on contributing and contributing", is probably a better description.
No I didn't see the programme, and yes it is inevitable that for physical or mental reasons, or indeed both, it makes no sense to force folk to carry on and on, using longevity as the feeble excuse to do so. I despair of those in positions of power. All they see is victims to push around in order to provide for the rest.
I do not, of course, infer that every aged worker is incapable, just that many and probably most can not keep up what they could achieve in their prime. And neither should they be expected to; they should be expected to make way for the next generation.