What's the point of scanning family photos at a higher resolution for later enlargement other than restoration?

With scanning, the DPI of the scan becomes the PPI of the digital image at a 1:1 reproduction. And 300PPI is about the limit of human vision for someone young with better than 20/20 vision (for most people/viewing conditions it's more like 200PPI). So the general recommendation was to scan at 300DPI and print at 300PPI... and that still continues today (although it is rather arbitrary). That's what the LoC post is saying.

Scanning at a resolution higher than what is contained in the image will not result in more detail. I.e. if your picture is of a white wall there is little detail to resolve, so there is no point in scanning it at higher resolutions. But if you scan the image of the white wall and print it at less than ~ 100PPI output size the resulting image may be obviously pixelated.

It is theoretically possible for a negative to contain more than 20,000 DPI/PPI of resolution (1.3 micron airy disks at f/1); but something like 1000-2000 DPI/PPI is much more common, and at something less than 1000 DPI/PPI is where an image becomes apparently degraded (unsharp). But that is at the negative size... at the print size the PPI/DPI is much less. i.e. a 35mm negative (or FF sensor) requires 7.25x enlargement to create a 10" print; and that 1000 DPI/PPI at the negative/sensor results in 138 DPI/PPI at 10" display/print (approaching readily visible degradation).

Another way of looking at the scan resolution is as magnification... if you want to do very fine/detailed restoration edits it can help to work at a higher magnification (w/o pixelation); and a 600DPI scan will be 2x the size as a 300DPI scan when viewed at the same zoom level (and when reaching pixelation). Part of the reason for editing at such resolutions/levels is so that the individual edits (dots/lines/etc) become "invisible" when the image is finally output at a lower resolution.

Whether the image is in color or B&W doesn't change any of this, nor does doing color separation. There is no benefit to scanning at a resolution higher than what you need; but there are definite negatives to scanning at less than you need. For most the question really becomes "do you know what you actually need?" And the answer is often "no, not really."... so scan higher.