Try working in one. The UK Post Office is trying to be a bank. I own a post office and can't sell euros to customers I've known for over 10 years if they don't bring ID. I used to just type in my own ID numbers to get past it, but even that doesn't work any longer. It's insanity.
And the amount I get paid for transactions? Not worth my time AT ALL. At least the tellers in your bank are on salaries. I'm on commission. Do I smile? Hmmm. Sometimes. But if I get grumpy because the system is ridiculously fubared or because the customer is being understandably belligerent, you can understand why! Ha ha.
Oh man, I'm so sorry, that must be terrible.
USPS here has some functions, like money orders, but not much more than that... and honestly their service has never been too great to be honest. So, if they took on more, I'm sure it would drive people up the walls.