Inverting Amplifier Not Applying Gain to Bias Voltage
When I simulate a circuit like this, I get exactly what I expect. The only difference is that there is no decoupling capacitor before the op-amp. Why does the removal of the capacitor cause such a difference?

Because with the capacitor, considering your 'V3' source as the input and considering the DC behavior, you have this circuit:



simulate this circuit &ndash; Schematic created using CircuitLab
So what is that circuit? It's a voltage follower with a gain of 1, exactly as you observed.
When you add a 2nd resistor that can carry DC current from the op-amp's inverting input to ground, you increase the gain of the non-inverting amplifier above 1. The two resistors form a voltage divider, which reduces the gain in the feedback path, therefore increases the closed-loop gain of the circuit.