The alternative to government supplied corporations is not much better: partnerships and conglomorates, whereby natural persons accumulate vast sums of wealth, individually or collectively. The government cannot forbid corporations from forming. It does not, however, have to recognize them. Individuals can enter freely into contracts which create partnerships and conglomorates. However, this ends up at the same place. Instead of individuals hiding behind a government-created fiction, they hide behind contract law, which cannot be abrogated without undermining the nature of law itself.
Corporations, by their very nature, are a legal fiction designed to circumvent that aspect of of the free market that punishes unconstructive behavior. Such an entity should never be created in the first place, if the leaders of a government had the intrinsic integrity to hold individuals accountable, rather than legal fictions. But the same legal fictions that protect the citizens behind corporations can also protect those who create the laws in the first place. Thus, corporations are the invention of lawmakers who themselves use said legal protections.
But this gets back to what TA rightly points out: Rand's assumption that the leaders of a capitalist system have integrity is false. But this is not necessarily a bad thing in itself. It becomes bad when that lack of integrity is joined to ideology, for the two are not mutually exclusive, or when it circumvents the very laws that establish said capitalist economy. If the problem were merely lack of integrity, then pure economics would take over - the government would succeed when the economy itself succeeded, and integrity would be irrelevant. That is the essential nature of capitalism: It assumes that because greed can never be eliminated, it is best to use greed to the benefit of everyone overall.
Ideology short-circuits this process. If, for example, taxation were driven entirely by greed, said greed would act as a sort of feedback mechanism. Taxes would automatically be set at the level that the market can best bear without being impeded by the taxes themselves, and thus driving down revenues. However, if instead the goal of taxation is not to make money, but to discourage certain activities, then ideology has trumped greed, and the government ends up with fewer resources than they started with, leading to higher taxes elsewhere, ad nauseum.
No system of economics is perfect, because people themselves are not perfect. Integrity and altruism can never be presumed. In fact, we should always presume the opposite.