It's also to speed things up. Many drivers want to hit their timetable; having to give change to 3 or 4 different people per stop is going to kill that.

The European busses solved that ages ago.

Driver presses the button for a special ticket, customer inserts coins or bills, the machine automatically gives exact change. Alternatively, pay with NFC, card, etc.

Or they have a small cash register and just give change back to dozens of people in the line, I've never seen a bus being noticably late because of it.

Honestly some of the things mentioned in here are mind bending. I have public transport experience from both London and a small country on the eastern side of Europe, and both were efficient, fast and safe. What the fuck is wrong with the US when people are scared to take public transport because they can get robbed?

Well, in some European countries the drivers do not handle any cash or tickets. Both for safety reasons and for the fact that having a queue of people waiting to buy tickets from a single driver introduces latency. Instead, there's a ticket machine on the bus stop, or sometimes inside the bus. Alternatively you can buy a ticket using a mobile app. This means you can board without a ticket. Then ticket inspectors randomly board vehicles to check peoples tickets.

There are vending machines that can give you change back. They should just pop some of those machines into the bus entrance.