Why is there a seeming dichotomy between mobility and photosynthesis?
The difference in energy requirements of a motile species make photosynthesis an unsuitable form of primary energy generation for them. 

Since plants are sessile, their energy consumption rates are lower. Plants have approximate respiration:photosynthesis rates of 0.35-0.9, as can be seen in this table (click to enlarge):



Once the energy consumption rates exceed 1, the organisms will, by definition, no longer be full autotrophs, as they will need to obtain their energy from alternative sources. Therefore, the relative low energy content of sunlight makes it impossible for motile animals, which have a larger energy requirement, to survive fully via photosynthesis.