[Donny Brook]

No offense, but there seem to be some of misconceptions at work in your analysis. I have some expertise in this area, so to be of assistance, below I have addressed where I think you might have some wrong ideas. Please don' take this as a general objection, just a desire to assist you on specifics.

Originally Posted by AlexanderHowl

... I do not think that current business models support such organizations,

There certainly are quite a number of successful and very large corporations, so to that extent current business models do support those at lease. If you are specifically thinking of corporations made up of a wide array of business lines operating as separate undertakings (let's call them 'conglomerates'), then there is some evidence that such structures may be inefficient or ineffective. General Electric is a prototypical example and it seems at times to be very successful and at other times to be barely surviving. One theory in management studies suggests that corporations should focus on their "core competencies" i.e. the few things they are really good at and the conglomerate model seems to diverge from that theory.

... corporate executives are more destroyers than creators

That seems like a pretty subjective statement and can be falsified as a general position by several counter examples like Steve Jobs, or Bill Gates.

and hedge funds like to dismantle the large corporations that they have purchased after forcing them to take on the debt that they used to acquire said corporations,

Many hedge funds have entirely different investing philosophies and many don't involve company stock at all. You are thinking of a specific kind of investor, the corporate raider, exemplified by the fictional Gordon Gekko of the movie Wall Street. Their premise is that a corporation is more valuable than is indicated by the market value of its shares and they buy up those shares and liquidate or disaggregate the company to get that value out.

corporate executives are only legally obligated to maximize shareholder value when the company is purchased and can otherwise safely ignore shareholder lawsuits.

Not really correct. Except in jurisdictions that enact laws to add other considerations, corporate managers are supposed to always be thinking about maximizing shareholder value. They are supposed to work for the shareholders and not any other interest. But they should be exercising some judgement about what approaches BEST serve shareholder value and over what time frames. A quick-buck-strategy may well be the opposite of shareholder value.

A megacorporation would then have a management culture that emphasizes stability, growth, and competition.

Those are frequent imperatives but not necessarily the only ones or the right ones for a given corporation. For example, growth and stability are often incompatible objectives, inasmuch as growth may require risk-taking or changes in practices. Another example, businesses in 'mature' industries are more likely to be focused on profit maximization rather than chasing growth.

In the case of stability, actions by executives that would destabilize the company in the long term, even if they are profitable in the short term, would result in summary dismissal without any compensation,

Summary dismissal without compensation is generally not legal unless dishonesty or insubordination occurs. Even gross mismanagement doesn't excuse the corporation from paying compensation earned, contracted for, or compensatory under law. There is also a question of knowledge. It is often not clear what effect a business choice will have until the outcome arrives. Often the decision-maker has already left or retired by the time the outcome can be discerned.

... and the employment contracts would stipulate such measures.

Well, they don't now, so while it is possible that such a change could occur it seems unlikely.

In the case of growth, the company would grow in one market until it reached the point where the expense of further market share would limit profits, then it would enter a new market while keeping the profit generation of the old market.

This is often true, though some companies don't get to the stage of seeking new markets, being content to simply milk the established business line. The writings of Michael Porter, Harvard Business School professor, might be informative for you on this subject.

In the case of competition, the megacorporation would expand through competition instead of acquisition, as acquisition just allows inferior executives to enter the organization.

The buy-or-build analysis is usually based on efficiency and value. While some companies are vulnerable to take-over because of inferior management, it is more often the case that they are targets because management has been excellent in producing something valuable but it has not yet grown so large that it cannot be bought by a larger or more well funded company. In many cases the inferior executives are the ones in the larger entity. You can probably think of cases where a good product disappears or becomes inferior after being acquired. Microsoft's purchase of Nokia is an often cited example.

Such a megacorporation would want to keep employees reasonably happy to promote stability, would want to limit legal entanglements in order to profitably maximize market share

Most corporations of any size will have that outlook. Though some thrive by squeezing their employees, particularly when the labor market is skewed against workers.

... and would use every legal and quasi-legal method to drive its competition into bankruptcy before acquiring its assets.

Actually that is not a productive strategy. If you want to acquire something valuable it is rarely sensible to destroy it first. Generally acquisition is a substitute for competition, not a follow up.

By keeping on the right side of the law, it would give the authorities no reason to look to closely at it, and it would toss anyone in its organization that is guilty of malfeasance to the wolves as a necessary sacrifice to keep the authorities and the public happy.

Two factors determine how true that is: (1) the basic integrity of the company's executives and (2) the effectiveness of enforcement and public awareness.

Additionally, it would likely promote from within, as it would value loyalty as much as it values competence, and would hire and groom talented people straight out of college.

That may be a good strategy, but there are successful examples that follow a flexible strategy or the opposite.

Now, such an organization would likely face stiff resistance from the established business community, as such long term thinking endangers the short term profits of corporate raiders and hedge funds, so they would need to effectively monopolize a new technology.

Frankly I don't think there is an obvious connection between one company's long term thinking and the short term profits of others. And again 'hedge funds' are so diverse in strategy and investments that it's not safe to generalize about them that way.

After the first such company reached megacorporation states (defined here as having revenues of 1% global GDP or greater), other large corporations would adapt their structures in order to compete.

Currently, the largest company by revenue is Walmart at 0.6% of GWP.
Companies will try to emulate successful examples LONG before one attains the levels you are describing.

Eventually, you would likely end up with a dozen megacorporations that control an average of 2% of global GDP each, a total of 24% of global GDP, with the remainder of global GDP being divided between governments, other corporations, NGOs, and the rest of the public.

Maybe, but that seems entirely conjectural, honestly.