People who are short due to a genetic limitation in growth hormone--as well as animals--tend to have longer lifespans and a resilience versus metabolic disorders rather than the other way around. It's not really clear that an increased level of growth hormone--outside of calorie restriciton or fasting, is all that healthy. And in those cases, there's a stressor that limits growth in the calorie restriction/fasting, the elevation in growth hormone may ameliorate this, but isn't going to result in a taller/longer phenotype.

For a while growth hormone replacement was touted as sort of a fountain of youth, this became less popular when exogenous growth hormone resulted in insulin resistance.