The short answer is: exactly this did happen with Red Gleam in the beta. Gleam was readily available in other colors on other worlds, so this issue was purely a cosmetic one. The devs are aware of this and I believe have learned some strategies to prevent them in the future. You can search for red gleam to get a fuller version of the story on these forums. I believe the user that was claiming them was called ‘nature’.
Most resources spawn in a type of block as part of a procedural world regeneration algorithm. This replaces mined blocks and will occasionally convert a stone block into a resource block/vein. This regeneration only happens if no player has come through an area recently.
The whole algorithm is fairly complicated, but in short an area that is very frequently visited won’t regenerate at all, and even an area that regenerated, but is revisited regularly will have fewer resources than one that has been unexplored for a long time.
I don’t know the details, but this is crudely how it works. Going to new places is better than revisiting old ones.
This means that claiming a resource-rich area to prevent it from being mined may have some small impact in the immediate vicinity, but ultimately the same resource will spawn elsewhere within blocks that likely have not been mined recently.
Back to red gleam, if all that is true, how did the red gleam get claimed and cause a shortage?
Gleam is (or was, it may be different now) different from other resources. Gleam is a base block type created by the world generation algorithm. Once a block is a rock, world regeneration will always make it a rock (and sometimes it will have a resource like iron or coal in it) but it will never regenerate into a tree. Gleam is like rock, it will always regenerate into gleam. A rock will never become gleam, just like a tree will never regrow as a rock. Because there was only a small amount of red gleam at a relatively small number of locations on one world, it was possible for most of it to be beacons by one user. Because gleam is a main type defined by the world generation, and not added by regeneration, it cannot be changed to appear anywhere else.
Additional notes, the devs have indicated that the world regeneration algorithm can be tweaked on live worlds, so something like iron regeneration can be increased or decreased to respond to gameplay conditions. Again, types set by the world generation (e.g. gleam or a rare wood color) cannot be adjusted (or couldn’t the last I learned about it).