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?