The logic of making you lodge a cheque, payable to cash, to a bank account and then withdrawing the funds from that account is simple. If the cheque bounces, all they have to do is debit you back, whereas if they simply give you cash from the till and debit their own cash account, they have no comeback on you
If the cheque is drawn on themselves then most banks should be able to check to see if there are funds there, regardless of what branch it is drawn on(perhaps PTSB systems don't allow this, I don't know).
If the cheque is drawn on another bank, they can ask the drawing branch if there are sufficient funds, but that branch is under no obligcation to tell them and indeed under their duty of confidentiality to the own customers, probably shouldn't
Remember as well, even if there are sufficient funds, depending on where the cheque was drawn, and given the length of time taken for a cheque to clear, there may still be a couple of days for a stop to be placed
Is a cheque made payable to cash legal. Very debatable as the definition of a cheque under the Bills of exchange act refers to a person or bearer, not to cash. However, it is a long standing practise for cheques to be writen to cash
Banks are very wary of cheques and drafts these days due to the amount of fraudulent items that are out there. There has been a spate of counterfiet drafts(which the bank is under no obligation to honour) and stolen/intercepted and altered cheques so they are right to be cautious