operational amplifier - Why use a transistor for getting a Constant Current Source in a circuit with an op amp?

I have used the above simple circuit for a constant source where $V_{\text{in}} = -5$V, $R_{\text{in}} = 390\Omega$, $R_f$ is the load which ranges from $110$ to $170\Omega$....would using this circuit for a constant current source for the load be recommended?

As current $$i = -\frac{V_{\text{in}}}{R_{\text{in}}}$$ $$V_{\text{out}} = -V_{\text{in}}\frac{Rf}{R_{\text{in}}}$$ so it should serve as a constant current source, but while browsing the Internet for a constant current source I typically found these sorts of circuits:

Is there a compulsion to include the transistor in my circuit? If yes, why wouldn't my circuit serve the purpose for producing a constant current?