I wonder if a similar idea would help with future costs for looking after the aged. Put $20k at birth into a pension account and just let it grow until they ret

I wonder if a similar idea would help with future costs for looking after the aged. Put $20k at birth into a pension account and just let it grow until they retire at 65. If they also put voluntary additional payments into the account as they work it would surely be a decent sum that obviates the need for the government to pay pensions to the retired.