I wrote:
"Current does not jump off the rails in a coil, it follows the coil wire
as it follows a straight wire elsewhere."

Wikipedia says, electrical conduction is the movement of charged
particles through an electrical conductor. The movement forms an
electrical current in response to an electric field.

Inductance is passive and though it opposes a change in current, nowhere
is the inducement to conduct any stronger than it is where the source
connects with the coil. The charges at the ends of a coil are going to
press on their neighbors to move on and keep the conduction going.

Inductance results from the magnetic field that forms around a current
carrying conductor. Electrical current through the conductor creates a
magnetic flux proportional to the current.

When there is an AC sinusoidal source, the phase of the current through
a pure inductance lags the voltage by 90 degrees.

Best regards, Richard Harrison, KB5WZI