There is also a capacity issue to consider.
Crossing through a departure stream impacts less on the departure rate, as that can be adjusted quite finely to give the crossers sufficient time to get across
Crossing through an arrival stream means that the arrival - arrival separation must include time buffers in case the crosser takes longer than originally planned to get across. You always need to consider the worst case scenario.
With departures, you may need to occasionally delay take-off clearance if a crosser is dawdling, but you only need it for those rare situations, not every time.
The other consideration, in line with the Prevention of Runway Incursion document from ICAO, is that runway crossings should happen at a low energy point of the take-off run (i.e. as close as possible to the start of roll, not half way down the runway).
Cheers.