Just as China will influence steel and aluminum prices through central planning, battery prices are unlikely to remain higher than current peak as long as the government continues its current stance on stable prices.
Regardless of whether the mines are outside of China, the refinement/separation step of mined raw materials is done mostly in China (>80% global capacity). In addition to the 3-5 year lead time of building the capacity through new refineries, there’s a significant process optimization learning curve (non-transferable learnings) to move down the cost curve for new refinery entrants.
On central planning, this is well known that China manages raw material prices according to the 5-year plan: https://www.reuters.com/article/us-china-commodities-idUSKCN...