Point: There is no correlation between age and performance / success. Performance and success are defined in terms of whatever is most meaningful to the specific individual. It could be a benchmark of health, wealth, wisdom, their combination, or anything else: competitively measured, appreciated in terms of self fulfillment, or a combination of both. For some billionaires whom I heard recount their stories: as they flourished more, it was just a matter of 'keeping score.'
Here is a verbal analysis of the above list. Some achieved high level of performance and sudden success at a younger age, Tiger Woods starting playing golf at 3. Some started from scratch in their 40s and achieved success over the next 10-20 years. Bloomberg lost everything and started on his success story when he was around 40. Simmons was an academic until around he was 40 and launched RenTech.
Lee Iacocca was fired when he was 54 by Ford, before he took Chrysler to its helm and turned it into Ford's archrival. In contrast, some had best performance as they grew past 20s and 30s, and into 40s: they are the best at their sport in 60s and 40s while beating competitors in their 20s and 30s. Ergo, there is no correlation between age and performance or success. Some achieve success young and later loose it all: those are not in the above list. We are familiar with examples from the recent events in the corporate USA and the Wall Street: how the Big-8 in Accounting is now Big-4 and how the Big-5 in investment banking will be recounted after the dust settles from the current storm.
Many can and do perform at a higher level even as they age past 20s, 30s, 40s, 50s, 60s, 70s, and few even past 80s and 90s. They seem to embody what some notable person said about excellence: Excellence is a habit. Some may call such individuals 'lucky' or 'outliers,' and perhaps some of them are. Many wait for a lifetime to stretch themselves to the next level, to a higher level of performance and success. Others just drift, sadly, waiting to start exerting themselves to perform and succeed at a higher level tomorrow or next week which sometimes never comes.
The reference to political leadership needs some qualification: the specific hint was to individuals such as the young Ivy League graduates in their 20s and 30s who occupy senior positions of power in national governments such as in Colombia. There are and were other national government leaders, including women in their 60s and 70s, who were leading countries considered among the world's leading economies today. Some of them were known for sleeping four hours a night while heading countries with billions or hundreds of millions of denizens.