Sifting through the coins in your pocket, you will likely find many images of politicians. In some sense, this conveys the impression that government leaders are the most important figures in society. However, everyday currency can honor other contributors to society. For example, check out this 50-cent euro coin featuring Miguel de Cervantes. Or these 20th-century physicists on currency. European currency lavishes less honor on political leaders than American currency (perhaps because almost all "great" European leaders have waged war on other European countries).
If we were to rethink which professions should be honored, we might consider where additional talent would most benefit society. This seems unlikely to be the political sphere. Imagine a world where twice as many people vied for political office. This would yield little social benefit.
Regardless of how many people vie for a political office, only one person will be elected. Political office really is a winner-take-all field. More capable candidates would lead to more capable officials, but this effect would be mild.
If both Democrats and Republicans became more capable, they could hypothetically reach more intelligent compromises. But it seems that a lot of political ability is used to misrepresent opponents in clever ways.
Most political differences are not caused by one side solving a difficult technical problem that eludes the other side. Much of politics is a zero-sum game because Democrats and Republicans simply want different things.
The actions of politicians are constrained by the demands of relatively uninformed voters. Simply making politicians more capable probably isn't enough to change the system.
If government leaders were demoted from currency, should artists take their place? Most people benefit greatly from artists; however, attracting additional talent to the arts might yield little incremental value. If Mozart and Wagner never existed, most of their current fans would spend more time listening to Verdi and Puccini. There is simply too much music and literature for any one person to consume in a lifetime. Additional artistic output largely steals attention away from other works of art. Many people write novels and compose music for the sheer pleasure of creation; (at least) the socially optimal output of art is already being supplied without providing additional encouragement. In the past, paying to self-publish a novel was considered a vanity project. Now there are so many fiction writers that trying to get any publisher for a novel could be considered a vanity project.
How about the fields of science and technology? Additional effort in the fields of science and technology would yield significant incremental value. Every scientist relies on the contributions of those that came before her. Miniaturization allows for faster processors and better manufacturing techniques, which in turn facilitates further miniaturization. In recent times, scientists and engineers might have done as much to further the enjoyment of the arts as artists. For example, using a Kindle app, I can instantly download a huge selection of free literary works written before 1923 (since they are in the public domain). Many of these works are out-of-print and would be extremely difficult to acquire otherwise.
It may be obvious that I endorse shifting honor away from politicians and towards scientists and engineers. Towards this end, I have a proposal for a Norman Borlaug memorial. Notice that to keep construction costs low, I've repurposed a pre-existing structure.