Because frames are very similar to vanilla item frames, it may be more intuitive to use the same mechanics. I suggest allowing empty frames to be placed in the world. Paintings could then be inserted by right clicking an empty frame in the world instead of using a crafting table.

Framed paintings already have a leather texture on the back side. That could be copied to the front.

The thing is that frames without paintings cannot know which size should they be. I can use the same way that vanilla paintings work -- to keep the most space possible, but not sure if that's needed.

What do you think is a use-case for such frames? Or the ides is just to keep things consistent with vanilla?

The idea is to keep it consistent with vanilla item frames. It could simply pop off if there isn't enough space.

They could function like prettier vanilla item frames.

Revisiting this, I still think it's out of the mod's scope, and I want to keep this particular mod in very "strict bounds" of what it is. Something like Quark could have different wood type frames.