The only reason for this is to prevent stealing.
A bartender is supposed to give and tear a receipt for every transaction that's run through the cash register. If a receipt isn't torn, an employee (possibly the same bartender) could save the receipts until a customer requests one. In the meantime, he could just keep pretending to ring up drinks and pocket the money. Without going into all the details of how this can be done, suffice it to say that it's easy, in any system.
However, just because a bartender doesn't give a receipt doesn't necessarily mean he's stealing. It could mean he's just lazy, or he forgot, or it's really busy and he rings everything up on one receipt. These are all bad reasons for not giving you a receipt and are against policy, but it doesn't automatically equate with a thieving bartender. Also, the tearing thing is usually the rule, but not every bartender does it.