See my preface. The notion of "delivered charge" crops up pretty consistently in electrical engineering, and it almost always means "charge delivered to (some lead of) some component (while ignoring charge coming out of one or more other leads)".
If you're willing to do more math, and to posit a switch that magically opens when current drops to zero, without itself having any voltage drop, then you can get exactly the same results (i.e. -- the total delivered charge is limited by your desire or the total resistance in the circuit) by having the inductor charging up a capacitor (which will have no more net charge when the process is done than when it started).
Or replace the switch by a real-world diode, and find that the total charge that will flow through the inductor is limited by the diode's characteristics as well as the rest of the circuit.