I am going to offer a slightly different perspective.
I work for a management consulting firm, and we hire (arguably) some of the smartest people in the world who are usually good with both critical thinking and with the soft skills. It sounds like an easily accomplished task, but it really is not. Some of the most analytical and quantitative people in the world also come with personality quirks that makes them unsuitable for most client facing professions.
I have also had my fair share of experience interacting with CEOs, both big and small. And it has been my experience that among successful people (the way society values success today anyway), there are two key elements to being at the top.
One is strategic thinking. Not everyone is capable of it, no matter what people may think. Some people are great at focusing on one problem; others are capable of bringing in disparate problems together and finding holistic, long-term solutions. This is a non-trivial task, and one with incredibly devastating consequences in the event of failure (and people do focus on failure, which is understandable, but discounting the success of social, political, and economic progress is disingenuous and silly). A good doctor is great at one problem, but cannot bring to bear the breadth of their experience to handle a disease outbreak, which has much wider consequences.
The second is capital. Modern society runs on capital. You would be staggered at just how much day-to-day credit companies use to run. If the cogs in the wheel were to stop, they will close their doors in a week. Take away the access to capital and you will be stuck at status quo. And identifying which ideas and which cogs in the wheel deserve capital is also one of onerous responsibility.
And that is the real reason executives and people in financial services (capital) get paid as much as they do. It doesn't matter whether or not you are in private or public sector -- those jobs are incredibly demanding, not the least because the burden of responsibilities demands a far more diligent performance.
An entrepreneur can create new ideas, but to bring them to bear on market and to make a company successful requires a different kind of expertise. There's a reason even Google brought in Eric Schmidt as a CEO from the outside -- from having an IPO to exploring growth strategies, running a company is a rare and valuable expertise.
And I am pretty egalitarian (in that y'all muggles look the same), and yet, I would say that the value society places on strategic thinking and capital allocation is justified.
Now, is this sometimes done blindly, without regard to performance? Of course, and that is a structural problem (e.g. Wall Street). And are there other professions (e.g. scientists) who should get similar incentives, but do not? Of course, and that is a perception problem. But neither of those really discount the importance of the jobs many executives play.
And at the end of the day, there is certainly a trade-off. People in those jobs work with little sleep, work brutal hours, and find it difficult to make time for their family, let alone anything else. Most successful CEOs I know wakes up at brutally early hours (~4 am) and are stressed beyond repair. They trade a relatively structured, stress-free life for one that offers great risk with great rewards. And ultimately, that's what society rewards. No guts, no glory doc.
For every Associate at McKinsey or Goldman who burns through 80 hour weeks, there are others who settle for a 9-5 job with a cute barista girlfriend and play pool on the weekends. For every 20 year old who partied through college with debt, there are many, many others who scored perfect GPAs and had clearly defined goals in life. For every geek who started coding in middle school and dropped out and played Counter Strike, there is a kid who busted ass and made it in life. Intelligence only goes so far -- structure, planning, and hard work go a lot farther.
Whether or not you like it, success is cumulative -- and course correction is a lot harder later in life than it is earlier.