Aksai couldn't just randomly change to a better cultivation technique on a whim, right in the middle of his current cultivation realm.
Usually, one only opted for better cultivation techniques than the current ones they were practicing after they broke through their existing cultivation realm and entered a new realm.
However, the Stellar Greenwood Tantra was not subjected to these restrictions.
This was because the Basic Greenwood Tantra was derived from the Stellar Greenwood Tantra. As such, there were no issues or side effects if Aksai were to shift to the Stellar Greenwood Tantra.
Stellar Greenwood Tantra was perfectly suited for Aksai's current needs. It also had a positive effect on the elemental affinities displayed by his Spirit Root. His cultivation speed was surely going to benefit from practicing the improved version of his existing cultivation technique.
