Why isn't a 1 Farad capacitor equivalent to a wire in LTspice?
In SPICE, an AC analysis starts by doing a DC analysis to establish the operating point. In a DC analysis, any capacitor, no matter how large its value, is treated as an open circuit.

So, if you replaced the wire connecting to the op-amp's inverting input with a capacitor, in the DC analysis, you'd have no negative feedback. If the op-amp model has any input offset voltage at all, it will most result in the op-amp's operating point having the output voltage at either the positive or negative supply rail, that is, in the saturation state instead of the active state.

In the saturation state, the AC gain of the op-amp is very low, and as Adam points out in another answer, that is exactly what you observed in your simulation.