401k already covers more people than pensons ever did. and that is before we account for the pre-reform cases where the pension lost it all. (Though some 401k is lost to scams)
"covers" is pulling a lot of weight here, I know a lot of folks with pretty small balances, and/or who "had" to withdraw due to medical or other emergencies. They need a govt pension, otherwise we are going to have a lot of people on the streets.
I do not know how to get data for how much people have in 401ks. I do know a lot of people didn't have a useful pension back in the day too. Government pensions are too one size fits none though. If you want to retire when you are still able to work you have to save for yourself, nobody else will take care of you like you want.
I think we are in agreement on your points, I'm only stressing that we can't take an attitude of "sucks to be you!" if Social Security "runs out of money". Many folks will need this, no matter how they got to that point.