How to cover a gap between doors and hardwood floor?
The most common solution is to add "wood planks" to the floor, not the door. These are called saddles.  They are specialized moldings, usually about 3 to 6 inches wide with tapered edges. The usually are 1/2 to 3/4 inches thick.  They are centered under the door and reduce airflow and noise.

These are most commonly available in unfinished oak or pine:

 

They also can be found in other woods, prefinished, or matched to a floor system: