I have a master server, where I want modify operations such as UPDATEs to be LOW_PRIORITY so that they don't block SELECTs etc. This is better for end-user visible behaviour.
I have a slave server, where I do batch processing, and I don't care about prioritising SELECTs over UPDATEs. In fact, because the slave consumes the UPDATEs and executes them as LOW_PRIORITY, and the replication is single-threaded, what happens is that the batch processing tends to delay the replication.
Ideally on this slave server I would tell MySQL to prioritise the UPDATEs above SELECTs, so that the two servers stayed in sync, at the cost of delaying my batch operations a bit.