Big ups to this, it really needs to happen. Log basket has so few use cases that it barely justifies going out of your way to get as a conveniece.
The most ethical introduction of this would be that you can only right-click empty logs it when it's added to the full backpack.
This would further encourage skillers/newer players to learn F-keys (actual game mechanic teaching through skilling) by going to the equipment tab to empty into your bag.
This would also stop the log brace from being near useless. The wiki currently suggests players don't use it at all because it's so inconvenient to have to dialogue to use it, especially if you're doing anything that will interrupt the dialogue.