I wonder why runners wish to run on a hard surface when the recommendation to avoid injuries is to run on grass, which often is on either side of MUPs.
Having said that, if you ride MUPs, you just have to accept that there are risks involved, that you need a certain skill set to avoid trouble, and that you need to keep a higher level of awareness which can be helped by looking well ahead, anticipating what might happen, and using a rear-view mirror to see what might be coming from behind.
The worst MUPs I've been on for traffic density have been through parks in Adelaide on a sunny day over the weekend. Melbourne's paths aren't so bad as most of the users seem to have a sense of where they should be.
It's not my favoured way of riding, and if there is a parallel road option, I will use it. But sometimes the path is a good way to bypass difficult conditions on the road or to take a shortcut.