The parameter "hfe" is hard to control. It varies with value of collector current, with temperature, and with speciman. Even if bjt devices are selected to tight tolerances, the temperature variation can be substantial. If hfe = 160 at room temp, 25 C, then it can drop to 100 value at low temp, -40 C, and increase to 300 at high temp of 100 C.
Generally for operation in the active region (linear amplification), emitter resistance is used to provide degenerating feedback. This nulls out variations in stage gain due to beta variation (beta is "hfe").
The same is true with gm, r_pi, etc. By using a good bias network, the amp stage performance varies very little with speciman, supply rails, and temperature. Have I helped?