They simply wont be able to pull it.
Today's workers dont have access to the much better defined benefit schemes a significant chunk of today's pensioners had - and because of poor performance of stock markets in recent years peoples pension pots haven't grown enough.
The mandated 4% employers have to pay in simply is nowhere near enough for someone on a modest income to build up a big enough pot.
Most people in their 40's today might have some private pension as a result of the law changing and mandating them, but for loads of those people, especially women who worked part time around children, will be lucky to accrue enough of a pot to secure a pension of maybe 6-8k which is not enough to live on. Even a £200,000 pot buys you an annuity of at best £7-8k.
Furthermore, more marriages and relationships break down these days so more people will enter retirement single, with more costs to be paid from a single source of income.
Many will still be paying a mortgage right up to retirement due to high property prices so will have less opportunity to save through their 60's.
There's no way they will be able to get rid of the state pension. Most people will only achieve even a modestly comfortable retirement by combining a state pension with a small private pension of say £8k giving an individual on their own an income of maybe £20-21k while a couple may have 40k between them. In neither scenario will they be living a particularly lavish lifestyle.
The real winners will be the few people out there now still in defined benefit schemes, though most are nowhere near as generous as they once were so even these wont support an affluent retirement unless the person was on a high income throughout their career eg a doctor or senior leader teacher etc.