It is the use of sugar that is recommended for the preparation of kombucha drink (white crystal sugar, cane sugar, rapadura sugar,
etc.). The beverage requires sugar in order to ferment and stay alive. On the other hand, during the fermentation process, the sugar is converted into lactic
acid and alcohol and at the end it is completely transformed.
Regarding the honey, this is a bactericide and therefore it could introduce composition changes in the beverage obtained and also it leads to the progressive loss of the "fungus".
It will happend the same if you use sweeteners: kombucha strain is exhausted and dies slowly.