If they got a lump sum, then that will be back pay from the period between applying and actually being awarded.
The fact they survived that interim period does not mean they are not in need of the money! If they've gone without equipment/services they required for say a year or two they can't go back in time and pay for them with the lump sum!
And if they lose their PIP, you, the taxpayer will not see that saving personally. You won't get a tax reduction, just some other area of tax spending will go up.
I had a big lump sum in back pay from my change of circumstances review - it took 19 months! In that time I cut back on our food and fuel use, and used that money to pay for services and stuff. When I got that back pay we got to go back to having three meals a day not two, and eating fresh food, because the weekly income had gone up and it went into my savings for the next big purchases. I was lucky not to go into debt, if I had, the backpay would have repaid it, but should we REALLY be saying 'if you didn't get into debt, you don't get any back pay'?