I would suggest tendering exact fare is comparable in time to using a bank card or smart card to pay for it, especially if you have to wait for a paper ticket to come out. The only time saving therefore would be in the change giving.
When you ask for a ticket, the driver has to find the fare on the ticket machine. That can take a while in itself, depending on the complexity of the fare structure. This is of course quickest in a flat fare system, but if you have flat fare then you might as well store the single fares on the smartcard and then you don't need to speak to the driver. This also partly works in a near flat fare system like Brighton, where the highest and most used fare can be stored on the smartcard, but lower fare(s) need to be paid for in cash. This is reasonably acceptable if not many people do short hops.
Without flat fare, the driver locating the fare on the ticket machine can be as tedious as the cash handling part if the route is long, there are many fare stages, and the driver has to work out which fare stage to use.