Why does current not increase when the voltage increases in this case?
The equation you say is the one imposed by the external components that accompany the BJT, not an equation that describes inner behavior of the transistor. That graph shows the relation between Vce and Ic, for particular Ib.

The equation you show to calculate Ic can be drawn as a straight line, therefore, the point where the transistor will work is the point where the both plots, the straight line and the other curve, intersect.

I recommend you to ask this questions on the Stack Exchange forum dedicated to Electrical and Electronics Engineering for a better range of answers.