Most "billionaires" contribute to both major parties to have influence on who ever wins.So it is…..
In theory "billionaires" do not have control on voting, ballots cast and/or ballots counted.
"Billionaires" become such largely through successful business dealings. Politics plays a minor role in affecting how to create wealth, but politics doesn't create wealth (it does redistribute wealth by taking from some and giving to others.)
To paraphrase the Bard's; "The fault dear Brutus lies not in our stars but in ourselves ..."
The fault lies not in the USA system, or that two parties have the majority of support, voters, and positions; but in the voters* who only think, vote, and act in a binary way politically.
*Barely half the citizens who can legally vote usually do so, which in effect means that barely more than a quarter of the citizens decide election outcomes.