Pensioners are as diverse in terms of wealth and income as working age people and in discussing such things we do run the risk of grouping pensioners into one single pot.
Some have more than enough, I look at one of my neighbours, both ex headteachers at large secondary schools who seem to have more money than they know what to do with, off on long holidays to very expensive destinations, built a large extension on their already big house and pay their kids an allowance every month. Neither of them came from wealthy backgrounds or had big inheritances. Good on them, they worked in senior positions, built up a good pension within the scheme available and on the surface seem to have a great life.
Others like my mum for instance have the old state pension and a small amount from my dad's final salary and whilst not rich, she gets by because the house is paid off. If she was living in rented accommodation her situation however would be much worse.