It is just another daft example of a council over reacting to a non existent problem. The quote given suggest an overtly anti-cyclist attitude “In the summer the park is heaving with young families. The potential for accidents must be huge.” Why??
There is also a yet to be resolved issue with the legality of these signs are they may conflict with the Land Reform (Scotland) Act 2003 establishes statutory rights of access to land, including for cyclists.
There is a need for education here, there are responsibilities on all sides, cyclist not to go through these shared areas at high speeds and families with young children to keep the children under control. There is no reason why there should be a huge potential for accidents...