IMHO they did this because that was the only incremental way to improve strength. They always relied an a fast search with a relatively simplistic eval function. For this approach alpha beta search works well. What is not clear whether it works well for the Leela approach. All attempts so far at least have not been successful(could be for other reasons, such as training approach). SF strength seems to be their well optimized search function. Rewriting that would IMHO be equivalent to creating a new chess engine. That being said I still think that the success of SF NNUE is very remarkable.