Yes you should let a wound breathe.
When you allow the wound to breathe the air that is allowed to get to the wound will promote healing of the wound.
However if you're bleeding then you need a bandage which is okay but after it stops bleeding then yes you should remove the bandage.
That way the wound can breathe and heal faster and better.
When your wound starts to scab over it's a good sign that the wound is healing.
A scab will eventually fall off the wound on it's own within 1 week to 3 weeks depending on how severe the wound is.
The wound scabs over because the scab on the wound helps protect the wound.