Why does so much current flow into circuit?
A real circuit would have a power supply capacitor and this capacitance is needed because real opamps need them on their supply pins. Now, if you looked at the current taken from the voltage source supplying power you would not see those high peaks.

However, this sim is not the real world and, more than likely, the model for the opamp is not perfect in every way. Last on the list is designing a model that takes the correct current under all circumstances.