Can't they just reduce the tax we pay and instead state that everyone is responsible for their own pensions, so if you save up enough you don't have to work longer...
Because you cannot expect all of the population to individually make wise financial decisions spanning multiple decades well past the years they can even generate income if they wanted. A lot of people already have problems budgeting for next month.
Because spreading out the "risk" of living much longer than you anticipated prevents destitute 95 year olds.
Also, on the more utopic/hippy views, it is just nice to help others, so why not institutionalize/codify helping others.
It is worth noting that if your goal is just to handle the people who didn't make wise decisions when young, the current system does more than needed, and there's a much better way to accomplish that. You can simply force people to save n% in a retirement savings account, managed by the government; ie. take the current system, but keep everyone's money separate rather than merging it into a common pool. This is how Singapore's Central Provident Fund works.
The current system really solves 2 problems: people who choose not to save enough, and people who didn't earn enough to save enough. You can solve the 2 separately: the first with the solution mentioned above, and the second with something like a negative income tax.
Now, the problem with separating the 2 is that there may not be enough political will for the second system, because it makes it obvious that the amount you receive in retirement is not in proportion with what you contributed. That's the case now too, but it's obscured by the structure of the program.
Life is about happiness - it isn't about work.