The simple answer:

If you wire a coil with a diode backwards:
- the diode acts as a short circuit
- the drive transistor overloads, and melts into a short circuit
- the fuse blows

Now, you replace the fuse because it blew and you have coils that are out.
- the shorted transistor passes enough current to open circuit the diode
- the coil is now permanently on, overheats, smokes.

OR
- the fuse blows again
- you replace the transistor and the fuse
- the shorted diode blows the new transistor and the fuse again
- You repeat until you figure out that the coil diode is bad, or the diode opens

And yes, the diode is there to absorb the giant "electric shock" that a coil generates when its power is cut (this is how electric shock buzzers work). WPC machines have this diode on the power-driver board. Flipper coils have diodes because they generate a huge spike that we won't want to carry around the machine.