This is correct. My own sequence was collect final cheque, cash it at Emirates NBD in atrium (only branch that will at that point) and then wire it offshore via Rostamani which had the best exchange rate to USD anyway. I was a longstanding Rostamani customer and I had the Rostamani customer ID card which negated having to present UAE ID and passport as it was already in the system - perhaps you should register for that before you turn in your passport/UAE ID for visa cancellation. Then the Provident was wired about three weeks later, in USD, to the same offshore account. I kept a couple thousand AED cash for expenses of the last couple days and then converted the residual of THAT at the airport. (As a backup I had one credit card from my home country but I didn't need it). What a good feeling to have NOTHING left in dirty-hams!
GBP/EUR PF currencies may have slightly different requirements, but I can see no need to ever cash and carry your PF balance, or retain a bank account until the very end. Unless you have a very specific reason, I personally wouldn't leave a UAE account of any kind open as a loose end, as they'd probably try and collect fees from you for something down the road, incompetent as they are. If you were transiting DXB for some reason that could be problematic.