You Can't move something you already placed so your going to have to delete the unit and spawn it in again

For most units and objects (excluding special entities like the player), you can select them and either press Ctrl + D to duplicate them or Ctrl + X to replace them at a different position.

To "move" the player, you can just place it again by pressing the button in the placement menu. The player's equipment will stay the same.

Is there some technical reason why simply being able to move something you've already placed down isn't a thing? Because that seems... sub optimal.

When you place an entity (doesn't matter if unit or object), there are certain rules for placement depending on the kind of object. You probably noticed that already. These rules ensure everything is placed on top of or snapped to other objects and not in unexpected places that could lead to issues while playing.
You can argue that using Ctrl + X and placing the exact same object where you want it to be is more or less convenient than moving it with 3d axis handles known from other 3d applications, but ultimately it's just a slightly different workflow that ensures everything is placed according to the rules.
Even if moving with 3d handles was to be added, it wouldn't allow you to place objects in arbitrary positions. Instead it would add more technical complexity to the game's editors.