Antitrust laws are indeed inherently anticompetitive.
First off, we have to note that monopolies are not inherently bad. They are neither inherently bad or inherently good; they simply are. For instance, a small town in rural America may only have one drug store. That drug store certainly has a monopoly on selling drugs, but it is not bad--people need drugs, and the small town market may well not support an additional drug store. An additional drug store might cause both drug stores to go out of business, which would be a net societial loss.
The only "bad" monopolies are those monopolies that are coercive--or, as is referred to in today's economics, those companies with "market power;" i.e., an ability to raise prices to supracompetitive levels. BUT, in a free market, the free flow of capital acts as a check on any company's ability to institute supracompetitive pricing. As a company with market power begins to charge supracompetitive prices, capital will shift to that particular industry because it offers a higher rate of return than other industries--thus encouraging new entrants, which will, in turn, lower prices to competitive levels.
A common response to this from Big Government types is a need to regulate "predatory pricing," which, in theory, is where a company that is faced with a new entrant lowers prices below marginal cost in order to drive the new entrant out of business which would then allow the existing company to raise prices to supracompetitive levels. Again, though, the free capital market prevents predatory pricing--an industry offering a higher rate of return attracts capital and new entrants, and a company cannot continue to engage in predatory pricing indefinitely. Indeed, even modern economics and antitrust law have recognized that predatory pricing is essentially impossible and you can really no longer state this type of antitrust claim.
More importantly, the concept of cross-elasticity of demand also makes it very difficult for most market players, even if they are to have a "monopoly" in a particular industry, to have a coercive monopoly. Any attempts to raise prices to supracompetitive levels will result in consumers switching to a different, less expensive (but equally useful) product. For instance, if SC Johnson were to attempt to raise the price of Saran Wrap to supracompetitive levels, consumers would respond by buying tin foil, a lower cost substitute.
So the capital market acts as a regulator of price, and so long as capital is free to flow, then prices are kept at competitive levels. ONLY in situations in which government restricts free flow of capital (stock market regulations, for instance) or places artifical barriers to entry (for many years, telephone and cable regulatory schemes, for instance) can a coercive monopoly take hold.
Let's make no mistake about it: antitrust laws are not designed to "level the economic playing field;" quite the opposite. Antitrust laws are a response to capitalists who have suceeded and accumulated (not by any sort of force, mind you, but simply by offering a product that consumers desire) massive amounts of wealth. Antitrust laws are simply schemes to redistribute wealth. Like income taxes, they are a thinly veiled socialist shot at the wealthy. That socialists have managed to clothe their laws in a defense of capitalism is the ultimate coup.
I note, incidently, the people you named weren't monopolists, but had tremendous industrial rivals: Jay Gould to Cornelius Vanderbilt; Getty had numerous rivals in oil, not the least of which was Standard; Morgan was hardly a "robber baron," of course; indeed, he essentially saved the government from bankruptcy.