What you describe above, putting the signal into the emitter is known as Common Base mode and is not widely used.
The more usual method is common emitter mode where the signal is applied to the base with the emitter effectively grounded so that Vbe is modulated, thus changing the collector current.
No one (that I know of) designs common emitter circuits by contemplating the change in Vbe... they are designed on the base current & collector current, taking account of hFE or Beta, the current gain of the transistor.
As you say, the change in Ic for changes in Vbe is highly non linear.
I suspect this is the difference between the semiconductor physics approach to things & we rude mechanicals who have to get the job done...