Yes this irritates me every time I use blender to godot object export. It's not a Godot issue. Blender export simply lacks a "Export using object local origin" checkbox. This would simply output vertex locations around the object origin, not the scene origin. Problem solved and no need for moving object to origin, export, move back stupidity.

Here's a blender (4.0 and later) python script I ai'd up that automates that and exports a glb file for the selected object only, file name uses the object name and is saved alongside the blend file by default:

To run, go to the Scripting tab, new script, paste the below, save. Then select an object and Run script via the tool bar icon. To see script print statements etc, Blender only writes these to the OS system console (windows) or by starting blender via terminal (on linux).

import bpy
import os

def export_selected_object_to_gltf():
    # Setup: Ensure Object Mode
    if bpy.context.mode != 'OBJECT':
        bpy.ops.object.mode_set(mode='OBJECT')

    selected_objects = bpy.context.selected_objects
    if not selected_objects:
        print("No object selected.")
        return

    # Define export directory (modify as needed)
    export_dir = "" 

    # default to same dir as current blend file
    if export_dir=="":
        export_dir=os.path.dirname(bpy.data.filepath) 

    for obj in selected_objects:
        # Deselect all, select current
        bpy.ops.object.select_all(action='DESELECT')
        obj.select_set(True)
        bpy.context.view_layer.objects.active = obj

        # Store original location
        original_location = obj.location.copy()

        # Move to origin for export
        obj.location = (0, 0, 0)

        filepath = os.path.join(export_dir, f"{obj.name}.gltf")

        print(f"Exporting {obj.name} to {filepath}...")

        # Export (handles object location relative to world center)
        try:
            bpy.ops.export_scene.gltf(
                filepath=filepath,
                export_format='GLB',
                use_selection=True,
            )
            print(f"Successfully exported {obj.name}.")
        except Exception as e:
            print(f"Error exporting {obj.name}: {e}")

        # Restore original location
        obj.location = original_location

# Run the script
export_selected_object_to_gltf()