You can select a footprint, then right click and select: Special Tools / Create Array, but that function creates new footprints that are not linked to the schematic and I do not understand how that can be used in a meaningful way.
There is also an “Place Footprints” plugin, but I have not used it myself. Is this compatible with your: “without having to resort to scripts?”
Another method is to use the “Replicate Layout” plugin, but this needs a change of the schematic. This works by making a schematic sheet with a row of LEDs and then re-using that sheet for each column. (or swap “row” and “column”, whatever works best for you).
With the replicate layout plugin you can also automate most of the drawing of the PCB tracks.
KiCad-Nightly also has a “Pack and Move Footprints” feature that may help with the initial sorting. With it you should at least be able to separate the LED’s from the rest of the footprints easily.