Reason for USB power bank LED to be always on?
Leakage current. Older simpler designs leak current through the boost inductor and diodes. Ten bucks says that the led is dim when not in use and brighter when in use? That's because it's tied directly to VUSB instead of a dedicated control IC like newer designs. Since the battery is not disconnected, it leaks and powers the led. When the current kicks up, the voltage of the boost circuit will rise to the 5V it is set for, and the led gets a higher voltage and hence brightness.

Basic Switching Circuit:






simulate this circuit &ndash; Schematic created using CircuitLab

When the switching circuit is off, the battery's 3.7V still leaks through L1 and D1. The battery typically has a protection circuit (DW01 IC) + mosfets that will disconnect it when the voltage hits the Over Voltage and Under Voltage thresholds, but in normal voltage ranges, are not affected. The battery is never disconnected.

It's not a minimum load for regulation, as that only matters when the current to a load is significant. While leaking it will be a milliamp or less.  It is actually discharging the battery unnecessarily, just very slowly. It's a bug in the design.