Without that dip/trap, you might end up with constant circulation and waste energy. Since hot water is lighter, it wants to rise, but by having that go down, you only get some conduction (you could insulate the pipes), not convection.
As piped in that diagram, you've also got a tap of untempered water which works quite well for things like a dishwasher and washing machine. That extra bump in temp can make a huge difference in how clean the dishes get and how well the detergent disolves. It may not be an issue if you have a heater in the DW, but using that will lengthen the cycle times - same thing on a WM, if it has the ability to heat water (some do for a sanitizing cycle).