Football at SPFL level takes up a lot of police resource at the weekend so the SFA probably took that into consideration with the authorities given the police presence in Edinburgh today for the arrival of the queen's body it wouldn't surprise me if this was a massive factor. The WoSFL and South Challenge Cup Committee took the lead from the SFA on the decision and probably didn't have much of a discussion about it and always planned to take the lead from SFA.
Whether we agree about it, it's all about being seen to do the right thing, so the lower leagues wouldn't want to be seen to do the "wrong thing"
The big question will be, will next weekends games go ahead? Country is a "National State of Mourning" and will be next weekend too, so would be odd to decide this weekend isn't ok but next week is