Unless they're late because they've been pootling along or sitting at bus stops picking their nose, I don't think that is particularly fair on the driver. Issuing refunds because someone took exception to a bus already struggling to keep time, for whatever reason, being made let by some pillock trying to get on with a ticket by another operator, waffling on about it for a while, deciding that they'd find out how much it cost for the correct ticket and then changing their mind anyhow (this did happen a couple of weeks ago - took several minutes and did make the already busy bus a little late) is going to make the bus even more late.

I fear it would also subject a driver to penalties for issues outside of their control.