Before the current, flat rate, pension was introduced, about 20 years ago, there was far more means testing in the system. This resulted in just the kind of resentments you can see in this thread about UC. It would also prove a significant disincentive to save for your retirement, unless you were likely to be able to save enough that the state pension was irrelevant.
If you consider two people, reaching retirement age, who have both always worked in similar, low to moderately paid jobs. One has always saved for their retirement and put aside as much as they could afford. The other, had far more fun when young, and spent their money on holidays, evenings out etc.
With means tested pensions, the one who had saved, but hadn't earned enough to have a lavish pension, would get little or no support from the state pension but wouldn't have been able to save enough to enjoy a lavish pension. They'd end up with much the same amount as their neighbour who had frittered their salary away throughout their life.
With a flat rate pension though, the person who has saved for their retirement gets to enjoy a more comfortable old age than they would if they'd spent the money in their youth.