What are the disadvantages of using a diode bridge for DC polarity?
The main problem with a diode bridge is the fact that you always have two diodes in series with your circuit, and this creates a voltage drop of about 1.4 V between the power source and the load.

The power loss is simply this voltage drop multiplied by the load current.

It also means that you cannot connect the negative side of the load, which you might ordinarily consider to be "ground", to any external ground, which might be connected to either side of the power source.