Why three fuses?
It depends on what you want to protect from over current. For the sake of argument, let's assume the controller draws 30 Amps at full power, and we use a 30 amp normal blow fuse.
The fuse to the controller is to protect the entire system from a controller caused overcurrent event. If the motor winding gets dead shorted, the controller will try top draw 100?150? or so Amps, and the fuse blows in less than a second. The FETs can probably stand that mistreatment for a very short time. If the short is less well made, maybe the controller tries to draw 50-60 amps, and the fuse blows in 10-20-30 seconds or so. The battery fuses don't get blown. So why have them?
The fuses on the batteries is to protect the batteries from a battery fault. You and I would never do this, but let's imagine that "Alan" meant to charge both batteries, but failed to turn on one of the chargers. When he connects the batteries, the first one to be connected will charge the caps in the controller to some level depending on which battery he connects first. No big deal. But when he connects the second battery, we now have a set of cells at 57 Volts supplying charging current to a battery that is at 40 some volts. Guess how big the current pulse will be! We effectively have a short across a 17 Volt battery. We can also guess that the 50? 100?150? Amp charging current will not doing anything good to either battery, but large reverse currents are generally bad for most cells.
If we just had fuses for each battery, and none for the controller, in the case of a motor fault, we would have to blow both of the battery fuses before power was removed to the controller. In dead short, they would blow pretty quick, maybe not as fast as a single, but still pretty quick. Probably the 200?300? amp pulse will damage the controller FETs. But if we got a not so good short, drawing 50-60 Amps, neither fuse would be drawing enough current to blow. Is a fire going to improve the short enough to blow the fuses? I don't know.
What I do know is that I paid $2.90 for 5 fuses yesterday, and it is cheap protection for a kilobucks worth of battery , motor, controller and work.
Regarding fusing only the controller outputs , I would point out that if the controller itself fails, you have no protection. My personal experience is with two MP3 internal controllers. One of them developed an internal short, and the other had the motor windings short. The fuse on the input side blew both times.
Please feel free to ignore any and all of the above, and do what you think is right for you.
TTFN,
Dennis