It's probably not the most efficient method. However, in general, methods that converge faster tend to lead to slightly worse minima (think momentum-based methods vs "plain" SGD), which "intuitively" makes some degree of sense (the additional time spent training isn't completely wasted, with some of it effectively helping explore the possibility space, optimizing the model in ways that simple gradient-following might miss entirely)

I would be shocked if there doesn't exist a method that does even better than SGD while also being significantly more efficient. But it's probably not going to be easy to find, and I expect most simple heuristics ("this seems to be helping, do it more" or "this doesn't seem to be helping, do it less") will lead to training time vs accuracy tradeoffs, rather than universal improvements.