Traditionally (at least in Spain) garlic was kept in a braided string, hung in a dry place, so that they could last until the following season.
Separating them in cloves will cause them to dry prematurely.
Breaking them apart to put in a jar - I see several issues.
You will almost certainly break through the skin on a good percentage of them as you separate them into individual cloves, meaning they will have lost their protective layer.
Unless the jar has some kind of desiccant, there is potential for the garlic to sweat & go off rapidly. The air inside ...
No citation, so not a 'real' answer; but common sense would say, "It's got air holes & it's dark" which makes it better than a sealed jar or glass jar.
Whether it's better than the cellar, outhouse or salad crisper in your average modern fridge… well, it looks pretty ;-)