Morgan,I don't know of specific diseases that infect Olives. I was speaking from experience as a Californian, seeing the orange groves every year getting pruned and the pruning piled and burned. I expect that is part of the rationale behind your areas approach to burning.
Of course, some men just want to see the world burn
I would also recommend processing the prunings through goats, as demonstrated in a recent Geoff Lawton video- they will eat the leaves and ramial (immature) wood, leaving clean sticks that will be ready for drying.