This is another evidence that transistor is controlled by voltage . When Vbe decrease then Ic decrease. The BIG question: Is transistor current controlled or voltage controlled. In your analysis you used current controlled. BUT C.B. show it otherwise. This is very tricky question : Which one happens first. Vbe or Ic or Ib? Right answer is : First Vbe should be there , then after that Ic flow. AND because of Ic , Ib will comes in So the true equation is : Ib = Ic/B and not Ic = Bx Ic . Ic must comes first then Ib not opposite.
A common base amp is VERY NON-INTUTIVE to have ANY GAIN! In fact it is kinda a reverse voltage follower which gains current. The CB amp reverse gains current to get SOME voltage gain. The only true use of this is it's HF performance and cascode configs etc. ...rare use cases.
