Those on the new state pension did not all work for six years longer than others. Many will have been in full-time education for several years after I left at age 16 (and paid for my own extra qualifications subsequently) so probably contributed for a similar number of years. My DH was 6 years longer in free education than me. He was even paid to be at University.
I was able to draw my SP at almost 62. I worked from age 16 (and at 72 am still doing some paid work) apart from about 3 years to raise tiny children (my first paid job after my first child was born was when she was 8 months old) and I combined part-time employment with self-employment meaning I paid Class 2 NI as well which qualified me for absolutely nothing. I claimed HRP for 18 years that did absolutely nothing for me most of the time either. For many years I also paid Class 4 NI which was basically another word for "Tax" - with no benefit to me. I also fell foul of the then rule that if you were employed part-time in many jobs you were not allowed to join the private pension scheme, until the European Courts declared this to be sex discrimination as the vast majority of such workers were women. BUT I had to pay over £3k to "buy in" 4 extra years of pension to make up the 15 years of part-time teaching contributions. I did get tax relief on them. I should have paid reduced NI during those years but never got the money from the government.
My DH now gets £100 a month more SP than me (old pension scheme as is mine).
I'm not pleading poverty cos I also have an occupational pension (greatly reduced due to being "forced" to claim it early), as does DH, plus three personal pensions (all paid for) and we also effectively had a third income between us due to a small business we had for about 25 years.
Like all government benefits there are gross inequalities, Some have occurred due to people making poor choices or doing nothing to try to support themselves in their old age. My best friend was one of these. Spent every penny of her earnings on luxuries (including several cruises), doubled her weight due to laziness, and accepted vast amounts of state benefits due to her poor health - that she was unable to spend cos she was housebound for years. I loved her to bits, but the result was that her two sons inherited all that unspent cash from benefits when she died.