Is Balance Training good for muscle & strength?

Yes — the evidence for this is strong. Balance and proprioception training has one of the more mature randomized-trial evidence bases in exercise medicine, because falls in older adults are common, costly, and relatively easy to measure. That's reflected in an evidence score of 76/100 for its role in muscle & strength, drawn from 9 studies (4 RCTs), with an estimated impact on longevity rated moderate (59/100).