In addition to the voltage, AC/DC characteristics of your PSU there are also transformer based PSUs and electronically regulated PSUs (SMPS).
While transformer based PSUs primarily suffer in terms of power efficiency with too small a load applied, SMPS units show multiple issues: not only do they exhibit decreased efficiency with too small loads but they also may not work at all from the beginning, cease to work after initially working for minutes or even couple of days (depending on power-on time, load etc.) or prematurely fail fatally. In other words, some PSUs need a minimum work load to operate at all/within specs/reliably.
For example, with one transformer based unit we needed to provide a certain minimum load for it to operate silently and within tolerable temperature range. Too little load and they would angrily humm and become quite hot in a short time span.
In another example, once we encountered an SMPS unit that simply would refuse to start up with two LED devices attached, one LED and one Halogen bulb would make it run however. Then another SMPS unit would only operate intermittendly with kind of a stroboscopic effect (est. ~1Hz).