That's not how respawning works. If a site is exhausted (i.e. shards had not yet respawned), then there are no shards, so there's nothing to target and shoot at. But once the shards are there, they are supposed to drop materials.
My choice of language may be an contributing factor here, so let me clarify.
When we enter a region like this (I did go watch the video, and it did prove to be what I suspected it might), those Crystal Shards are "spawned" throughout the region they occupy, can be targeted and shot.
The act of shooting them is then supposed to "spawn" a material that can be collected.
In this particular case, the shards themselves "spawn" and can be targeted and shot, but they fail (not all, but some) to produce (spawn) a collectible material.
This is consistent with my experience with an exhausted site, however I do not believe this is how this is intended to function, as with Geological Sites, the various shootable objects simply do not spawn in the first place.
I suspect one of the following to be taking place:
1. The materials to be spawned are generated from a list which contains a null entry, causing no material to spawn.
2. The material is being spawned, but either too far above or too far below the player to be seen. I have seen this happen with surface rocks where a material will spawn below the planet's surface and continue to fall away until it is out of range.
3. The targetable portion of these crystal structures is spawning when it should not.
