As an ex government manager, I don't think that would be the case. If someone is off sick for say, 4 or 5 days, their work might just be left. However, if they handed in a sick note for a month, you would absolutely have to (as a manager) redistribute their work.
What I found as a manager was that when I redistributed work, often the highly experienced staff would power through those additional cases (and then get allocated more) This was far more likely to account for the fact that some later cases appeared to be picked up first.
I hope that makes sense. It's still rubbish when we are all waiting. However, I think it's important to remember that they say roughly 18 to 20 weeks and that still seems to be the case. (Some lucky and hearing with a scan date of 5/9 for example, and some till waiting from 21/8)
If it ever got to the point where folk were being awarded months before others, then that would be very wrong. As it is, it's simply not that easy to have everyone working at exactly the same pace.
Their telephone manner and attitude is a different matter entirely, though. They should absolutely be hauled over the coals for that!!