Well it depends exactly how you factor things in, because those rich pensioners will then pass that wealth onto their children of course less the horrific amount of death tax to be paid first. So it all goes in circles anyway.
So children who already benefited from having better-off parents benefit even more by getting that inheritance, while a regressive NI tax disproportionately penalises those without that inherited wealth.
As for 'horrific' - it's not the 1950s. £500,000 tax-free threshold if you're passing on your home to your kids. And 40% above that.
Meanwhile, people who earn more than £50k in a year have to pay 40% on anything above that threshold, so you'll forgive me if I don't weep for those who have to pay a real tax rate of, say, 15% on an £800,000 windfall.
We are sadly not in the position demographically that we were when today's retirees were in the core of the working age population. We have a huge affordability issue here as people live longer, with more complex needs in that extra time. It's great they're living longer but placing a greater burden on generations that have already lost out in other ways (tuition, housing affordability, etc) is not a straight fix. A progressive tax should be the long term solution but in the short term, looking at affordability and unearned wealth as well as tax on all, not just those of working age, probably needs to come into play if it isn't going to be a horrifically regressive system.