Use via Inspector to script assigned public texture as default

Hey,

I have a script with a public Texture2D to which I assigned a Texture via Inspector directly on the script (not assigned to a gameobject yet).

I thought, that this could be used as default value, e.g. if I now drag and drop this script onto a gameobject, it will fill it automatically with the assigned Texture, or at least if I use AddComponent via script, the to the script assigned texture should be used. But instead the Texture is always null.

What is the use of assigning public members directly to the script? Is there a way of assigning such a default value for a public member?

thx.