Fires require a warm chimney to burn properly.
A chimney that is not inside the insulated fabric of the home, will be cold and therefore, difficult to light and it will probably not burn slowly without smoking.
A central chimney will disburse its heat all round into every room.
One thats part of an outside wall needs insulating on the outside.
A fire that does not have its own dedicated fresh air supply, will struggle to find air to burn, will create drafts, will be difficult to light and get going.
When a fire is lit, to get going, the kindling has to be hot enough to lift all the cold air that is inside the chimney up and out and push it to one side before the fire will start to burn properly and the chimney will warm up.
When there is an area of high pressure sitting on top of us, it is far harder for a fire to do this and often the smoke will billow into the room. (Most unpleasant.)
The first time you light a fire the chimney is very cold and damp, the fire needs to be alight for some time (and hot) to dry the chimney and warm it.
A four inch pipe bringing air from outside to the fire will make the start up much easier and result in a pleasant warm room.
Why burn the very warm air you have paid to heat up, when you can burn cold air from the outside?
Homes without a dedicated air supply end up with people being baked on one side and frozen on the other.