I think it is disgusting that you are not given a clean pot and the old one disposed of because if they are the non sterile ones, they cost pennies. Universal precautions should be taken with all bodily fluids, i.e. samples from boden-wearing mummies or prisoners or substance users should be treated the same for the protection of all. In order to ensure the sample test result is accurate, it needs to be in a clean but not necessarily sterile container. If you knew how much money is spent on specialist testing of substance users you would weep. I think it is poor show that they cannot spend 20p on a pregnant woman for the duration of her pregnancy.
I also have visions of folk forgetting it is in their bag, finding it five weeks later all putrid, trying to wash it out, or toddler finding it in the bag and pouring it in your shoe, or worse. Not that any of you lovely ladies would, obviously.
In clinics there should be a disposal system in place, either there or back at base, with a system in place for safe transfer.
If a mum is known to have Hep C, it is unlikely the pot would be given back. What if another mum notices that she gets a clean pot each time. And no, I do not have Hep C 
and other mums who have been given clean pots should not assume that either.
We all have things that irritate us, and this is one of them. Others are obviously entitled to their own opinions.