Should the UK Gov buy an index linked fund at birth for each person?

The UK's state pension is funded on a pay-as-you-go basis through National Insurance contributions from current workers to pay today's retirees. With an ageing population and rising costs projected to exceed £150 billion annually by the early 2030s, some propose shifting to a funded model where the state invests a lump sum in a market-indexed fund for each newborn to grow over decades. Similar ideas appear in discussions around baby bonds or sovereign-style pension funds, potentially reducing future fiscal burdens but requiring significant upfront government borrowing or tax increases.