With regard to your question is it necessary to have the moss washed of the roof?
This seem to be the advice
It is only in circumstances where these growths are interfering with the free drainage of rainwater off the roof slope should there be any cause for concern. In these circumstances it may be necessary to clean the roof tiles using a suitable, regulated biocide and a wire brush, or a low pressure wash.
Roofing experts warn that roof tiles should not be subjected to high-pressure washing or jet washing for many reasons which include:
Removal of Lichen and moss by jet washing will invariably remove the granular surface finish and potentially damage the structural integrity of the tile, this process followed by a surface treatment application would invariably invalidate any tile manufacturer’s guarantee.
Interlocking roof tiles are not designed to be walked upon, foot traffic can cause these interlocks to break opening the roof up to water ingress.
Inappropriate pressure washing can potentially force water up between the tiles and roofing felt into the roof space. Bedded mortar and flashings can also be blasted off sing this method, potentially leading to further costs for rectification.