It’s the path that maximises time, not distance. Technically the path that maximises time could look the same as the path that minimises distance, they could just sit down and wait decades until a minute before they die of natural causes and then get up and head to the end, and that’s assuming that they need to arrive alive.
This source is including many more causes of death not included in the US number. The average annual direct killings by the US police is 1096 (33.1 per 10 million), while the UK is 3 (0.5 per 10 million), about 66 times worse per capita.