DLA to PIP - confused about date PIP gets paid?

When I started the PIP process, I assumed like every other benefit, that if you got it, you would be paid from the date of the claim. It took 14 weeks for a decision to come through, which was 7 weeks after the date of my face to face, however my letter has informed me that by law they can only start paying PIP four weeks after the date of the decision. OK, I know I have been getting DLA in the meantime, however my PIP assessment puts me on a higher rate of payment than the DLA (standard care PIP when I had low care DLA), so in effect I have missed out on 14 weeks of about £25 extra a week. Is this policy something that is being challenged? First, the fact that my care needs were as I wrote them on the original application - they haven't changed in that time, so how can they not pay me the full PIP rate all that time. Second, that even though I know the ATOS report was with them within days (I requested and got it three days after the f2f assessment) it took SEVEN weeks for them to use this and make a decision - when if they had acted on it immediately I'd be seven weeks payment better off. I've looked at the letter, and it does seem that I don't have any grounds at all to challenge them taking 7 weeks to just repeat exactly what the ATOS f2f report said. It seems like they are really taking the mickey by dragging out decisions as long as possible when they are going to result in an increased payment.

Thanks for the reply. I don't think there is any point putting a complaint in to DWP. Its just another part of the whole PIP process that doesn't work as well as it should. I am thankful I got my award without needing to go through the appeal process, but they do seem to make it a much more stressful drawn out process than it needs to be, and I can't help thinking that they are delaying "yes" decisions because it saves them money.