The benefits of a pension start before retirement. I can avoid setting aside a huge pile of money for the potential of an extremely long lifespan and then worry as minor changes to that pile become really critical near and in retirement.
Suppose you’re 50 with 2 million USD in savings. How soon do you retire and what kind of lifestyle do you live in retirement? That’s heavily dependent on what kind of pension is waiting.
Where I am, we have personal pension plans. You can check "what kind of pension is waiting" by going to the pension fund website and checking. Gov't doesn't play any role in any of that -- except (a) prescribing mandatory monthly payments and (b) determining the retirement age. (You only get small gov't pension if you haven't collected enough in your personal plan.)
If it’s just a savings account, that’s not a pension.
Assuming it’s a defined benefit pension it can include guarantees like inflation adjustments. That’s the fundamental advantage which largely offsets the disadvantage of lower average returns.
I’m not saying putting all your money into a defined benefit plan is ideal, but due to the diminishing marginal utility of money a guaranteed minimum lifestyle is extraordinarily valuable.
It’s not a savings account. My employer and me both pay monthly installments to the pension fund which are tax free. The money is under my name, and is not used to cover any pension of someone else. I can decide where it is invested, and change it at will. Once I go into retirement, the accumulated amount is converted to monthly payments which I will receive until I die. If I die before the retirement, my children will inherit the whole sum.
In the way that (a) its establishment and monthly installments are mandated by law, at the rates prescribed by the law (which isn't the case for "a savings account"); (b) both the installments and the revenues are tax-free by the law (which isn't the case for "a savings account"); and (c) the law that establishes the fund, mandates payment on both employees and employers, determines the rates, and frees the whole thing from taxes is called "the Pension Law" (which isn't the case for "a savings account").
However if all of the above also applies to savings accounts in the place you reside in, you can call it "a savings account" all right.
I think this is very similar to 401(k) or IRA, or "self-invested personal pension", except that the law sets the percentage amounts for both employee and employer contributions.