I’ve found some old external USB drives and drive enclosures. Some of them, I found the power bricks and cords for, others I haven’t, and a few have cords damaged sufficiently that they are unsafe to use. For the ones where the brick is missing or the cord damaged, can I purchase an "off-the-shelf" brick-and-cord system and use it successfully, provided that the brick’s output (both voltage and amperage) is equal to or higher than that required by the drive/drive enclosure, and that I have a compatible plug?
Generally, yes, it would be okay to purchase a generic power supply for your device; there isn't a specific requirement that the device must have its original power brick/supply
When looking for a replacement power supply, the voltage provided by the supply must be approximately the voltage required by the device, although there is a tolerance, so usually it's no problem to e.g. supply a 5V device with 5.5V.
With regards to amperage/current, however, the device will only take what it needs.