I conceded to that, but at some point in time the current has to rise or we would never have any current to operate the motor. And when it rises it rises at a rapid rate. This time is apparently so short that without using specialized measuring equipment it seems to be almost instantaneous.
I was told there is no "inrush" current when a motor starts. Exactly how you look at this is all that is being mentioned as well as some terminology being thrown in the mix. Bottom line is even it it isn't at the same instant the circuit gets closed, there is a rapid rise in current at some point and sure looks like it is some point less then a tenth of a second, which is a long time with 60 Hz being the measuring stick.
Bottom line - there is a surge of current that flows at some point during the process of starting that motor that is higher then it's normal running current.
And I am fairly certain that it often is higher (though only for very short time) then what the motor would draw steady state at locked rotor condition.
The rapidity with which current rises through an inductance is adjustable through its time constant L/R.