IMO I think Obito helped kill the Uchiha clan because it was direct orders from Madara so he had to do it sometime so why not accept Itachi's offer.
The reason is because Madara intends to cast Infinite Tsukyomi and he doesn't want anyone getting in the way, the only way one can be released from Tsukyomi is if one had the Sharingan, if the Uchiha clan were still alive those in the clan who awakened their Sharingan to its full potential can dispel or maybe even break free from it. If this were to happen the Uchiha clan could retaliate or plan to either stop Infinite Tsukyomi or control it themselves.
The reason is because Madara intends to cast Infinite Tsukyomi and he doesn't want anyone getting in the way, the only way one can be released from Tsukyomi is if one had the Sharingan, if the Uchiha clan were still alive those in the clan who awakened their Sharingan to its full potential can dispel or maybe even break free from it. If this were to happen the Uchiha clan could retaliate or plan to either stop Infinite Tsukyomi or control it themselves.