Supplementing with eg Tris or Hepes increases buffer capacity so more stable to pH changing due to action of cells, chemical or biochemical reactions that produce eg acid.
On the other hand Phosphate is more stable to heat or light than synthetic buffers like Hepes.
If you are trying to simulate physiological buffers then you often have quite low phosphate concentration therefore not much buffer capacity. In vivo much buffering comes from proteins and bicarbonate so adding a buffer such as Tris or Hepes provides the extra buffering capacity needed