The economic concept you are touching on is called Division of Labor. Corporations are just a collection of individuals. Nothing magical transpires in terms of what individuals do when a "corporation" is "formed" or given "legal entity". It's still the same old individuals trading the same old things to each other.
No one person can do everything at anywhere near the efficiency compared to specializing and trading your own surplus for the surplus of someone else. This is exactly what goes on in the real world and in Vana'diel. If you like cooking but don't like fishing, you'll buy somebody's elses excess fish on the AH and sell your excess finished cooked goods on the AH. Likewise for someone who likes fishing but doesn't like cooking will sell fish but buy finished cooked goods.
Prices are signals of relative scarcity. What's one of the least scarce things in the game? Gil! More gil is created, was at one time vastly created in the rusty cap fishing era, all the time. That's one of the primary reasons the amount of gil people are willing to trade for other items seems to have skyrocketed. It's because the circulating gil in the economy has skyrocketed.
Corporations *are* individuals. Corporations in Vana'diel (in the sense that some worker slaves would be shielded from supply/demand pricing structure to make it profitable for the owner) would be vastly inferior to the individual production we currently have. Or it would be exactly the same, except certain individual players who buy and sell from specific other certain individuals would be given an artificial name as a "corporation. Are you going to pay your farmers an hourly wage, pay them per bushel, give them health insurance (raises if they die :P), pay them the same, etc. etc.?
Corporations in the real world get monopoly patent and copyright protection. That increases the price consumers pay. Could you imagine how expensive goods would be in Vana'diel if the first crafters of specific syntheses were granted exclusive production of them? Prices would be much higher. Thus, in Vana'diel you cannot control any market. You cannot prevent new entrants when after driving them out through low prices you raise your prices.
Why would any farmer, or any crafter want to work for you? You would have to offer them something better then they could get on their own. You could buy in bulk. But buying in bulk does not remove supply and demand. You won't keep buying in bulk at the same price once the price of your finished goods start dropping or end up not selling and being returned to you unsold. Thus you would "fire" some of your employees, or "lay them off". But the exact same thing happens with no "corporations" through the price established by supply and demand. You cannot lock anyone out of the beeswax market like you can in the real world by using government monopoly force to prevent and deter new entrants into your market.
Many people in Vana'diel have a job, at least part time, that in the real world would be similar to xeroxing dollar bills. Both in the real world and in Vana'diel the legally declared money supply are not established by the free market. People don't bury dollar bills in the backyard. Why would anybody ever trade some food or some land for some green and white colored paper (and you had no interest in that paper for artistic or other purposes, such as starting a fire)? Only because the government says you must. People would rather buy more backyard, or a second backyard. People don't store gil; they convert it to some "real" money bullion sitting in a safe, like a pair of cross counters.
It's completely untrue that the rich get richer and poor stay poor. Everybody gets richer all the time. Every single month pretty much every character has better gear or more stuff than they did last month. That ain't staying poor. Look at what you have now compared to what you had 10 seconds after you created your character, and imagine what you will have a year from now. Pretty much everybody will be better off in the future than they are in the present. Only in the worst socialist envious sense would people prefer to be more equal yet all wearing starter gear.
So to conclude, your premis that a "corporation resource" is lacking and contributing to skyrocketing prices is if not fatally flawed, severely lacking in eludidating the matter at hand. Individuals freely choose how much of one thing, such as gil, they are willing to trade for another thing. Anything, *ABSOLUTELY ANY* deviation from that state of affairs, would *necessarily* by definition make the sum total of subjective value less than it otherwise would be. People only trade because they value what they receive more than what they give away in the exchange. If someone is not freely willing to trade one thing for another thing, forcing them to do so is necessarily making them worse off. Only individuals trade. Only individuals value. Only individuals set prices. Nonetheless, rate up for an original interesting read.