Maybe you couldn't afford to? The low paid are often barely keeping a roof over their head and their family fed, it's not as if everyone has £100's a month to chuck into a pension scheme. And even if they do (I do luckily) the returns are not all that great. Frankly looking at my yearly pension statement I think I could probably do a better job with the money myself.
The state pension is there to ensure everyone who has worked and contributed to the common good via taxes and NI gets to live a reasonable life in their retirement. Not a luxurious life necessarily - as you say, if you want luxury, save for it - but they shouldn't feel hungry or cold or afraid. That's one of the famous 'social contracts' that keeps us all working together and supposedly prospering together.
If we can't guarantee a decent lives for our children (note the rising levels of child poverty) and we can't guarantee decent lives for our elderly, what exactly the hell
are we doing? And what are we paying those who supposedly run our society to do?