The circuit has the trend to stabilize operating point against changes in temperature and β-value.
In this type of circuit, to keep IC independent of β the following condition has to be met:
Ic = βIB = β (Vcc - Vbe)/ RB (β+1) RE ≈ (Vcc - Vbe) / RE
That is approximately the case if
(β + 1) RE >> RB
As β-value is set for a given transistor, this relation can be satisfied either through keeping RE very large or by making RB very low.
High VCC is essential if RE is of large value. This increases cost also precautions are essential while handling.
A separate low voltage supply should be employed in the base circuit if RB is low. By using two supplies of different voltages is not practical.