The two-party system of the US is more than an "illusion of free choice"

An entire institution is rarely justified by simply setting up an illusion for the average person to fall for. The US duopoly is a good example for this.

There is a very material incentive for the bourgeoisie to have precisely two parties alternating, that is, the importance of donors.

If the blue team were to lose only a small amount of donors, they would inevitably lose to the red team, and vice versa. If there were more major parties, losing donors could be a calculated decision to not alienate a part of the electorate, because the donations would go to one of the major parties. But in a duopoly situation, the donor's money go straight to the other party, doubling the relative loss. On the contrary, a monopoly situation is not ideal because the importance of donors is diminished since the campaign is less important therefore money matters less.

This system therefore ensures maximum control over political parties by the bourgeoisie, because it optimises the bargain that donors have over party politicies