I agree it's cool you thought of this without the background.. for sure.. even though you said you had a little.
You're right that the motor draws more current when it starts.
But you're wrong in saying it's BECAUSE it has to do work.
Only a motor with a drive is smart enough for that
For a constant voltage applied, like your 12 volts on your starter, the motor draws ONE current value (for a fixed temperature)
As any electric motor speeds up, it develops counter emf, which bucks the source voltage, and the motor has less overall current drawn.
That's why when you load a motor, it seems to TRY harder, really it only draws more current because the load slowed it down, reducing the counter emf.
PS a good test, is to take your car blower motor, and attach it to a 12 volt source, and hook up an ammeter. Notice, the motor draws the same current when starting, as it does when you grab the shaft and force it to stop.
That current is the locked rotor current, and it exhibits locked rotor torque.
It doesn't try any harder to move your hand than it does to start moving initially. entirely because of no counter emf induced in the armature.