I agree with the comments above.
All degree courses require that you have some basic skills such as literacy; they require that you can take notes, write essays etc. Here an access course is a good foundation and mature students often have other qualities which can improve their chances of an offer.
Some courses require that you have specific knowledge, such as mathematics or science subjects. Here the access course is unable to provide you with perhaps specific knowledge in specific areas. The variety of ‘A’ levels on offer will provide this.
So the implication of the question has truth in it. Some departments in universities do not see the value of the access course. However that does not mean that all departments feel the same.
To talk specifically of the LSE, I am doing Government and History, so my Access course provided me with most of what I needed, although I still struggled. Had I chosen to do any of the maths based subjects, my Access course would not have prepared me for the level they work at. I would not have struggled; I would have sunk without trace.
It is not prejudice against Access courses that determines their suitability for judging candidates. It is the experience of how students cope with the demands of their degree courses that shapes whether you are offered a place or not. Access courses do not always cut it.