Can I ask here?
As I see it would work only if I drop asset material on object in Object mode.
Let's imagine behavior for Edit mode:

1. without selection: I drop asset material on face, it should replace material slot under the cursor (as you mention in TODO).
2. with selection: I drop asset material on selected faces or even in free space or other unselected element, it should create new material slot for selection and assign dropped material.

And do not forget about multiple objects.
If I select multiple objects in Object mode and drop material - how it should behave? Replace material slot under the cursor for one object or replace material with the same name for all objects?

And for multiple objects in Edit mode.
As I explain in 2. + it should create and assign material for multiple objects.

Thanks.

@Eugene Du (APEC) I would say that if a user has already a selection and you want to assign a material to that selection dragging and dropping is already a waste. It would then be easier if there is an operator "assign to selection." The time saver of dragging and dropping is that you can do it without changing selection. An assign to selection could also work in edit mode. Although not a fan of creating new material slot or different behaviors based on selection I do see for editing this could be useful.

The current system is better prepared for material templates (eg assigning base materials that can will be modified by the user afterwards.)
For edit mode there are more stuff to think of. basically every time you assign a material to a selection a copy is created of the material. This is something that you don't want when in edit mode. If the object has already that material the system should be able to reuse that material. This is not easy to do in the current system as assets are applied and references to the original asset are removed. And what should happen if the user in the mean time has altered the material. Is it then still the same asset?

I will get some feedback from others and see what workflow should be more dominant.

In D12056#313055, @Jeroen Bakker (jbakker) wrote:

"assign to selection."

I'm not sure if it would be better than drag-n-drop.
How it would be implemented? RMB on material in Asset Browser and select option "Assign to selection"? or there will be the button somewhere in the Asset Browser UI? All two variants to click and to search for button will take the same time or even more than just drag-n-drop

For edit mode there are more stuff to think of. basically every time you assign a material to a selection a copy is created of the material. This is something that you don't want when in edit mode. If the object has already that material the system should be able to reuse that material. This is not easy to do in the current system as assets are applied and references to the original asset are removed. And what should happen if the user in the mean time has altered the material. Is it then still the same asset?

Can it firstly check for same names when we drop material, if names matched then select other faces with same material, reassign and select original selection.
About "has altered the material", if he change material name then yes, it's a new material and, when assigning, it should create new slot

I will get some feedback from others and see what workflow should be more dominant.

if you create topic on devtalk then definitely there will be many reviews and suggestions about it.