Gemini's and your conclusion is wrong. Arrow's Impossibility Theorem is only valid for ranked-voting systems."Arrow's Impossibility Theorem
"The theorem, developed by economist Kenneth Arrow in his 1951 doctoral thesis, mathematically proves a fundamental issue in social choice theory. It states that when voters are asked to rank three or more distinct options (or candidates), no ranked-voting electoral system can convert these individual preference rankings into a single, community-wide, ranked preference order while simultaneously satisfying a specific set of seemingly basic and reasonable "fairness" criteria."
Gemini goes into more details, but I just wanted to point out that having more than two political parties cannot result in fair elections.
The U.S. two-party system is bad because like in all countries, voters tend to distribute themselves equally around the middle, and when you only have two parties represented, the winning party will have only a tiny majority of the voters behind it (well, in the US system a party can even win without a majority of the voters behind it). This means that it is possible for the election result to dramatically swing from one election to another even though only few voters change their mind. I say "dramatically" because the two parties have to have very different policies in order to encompass their own half of the voting population, and the result is political instability.
If there were multiple parties, a single party will seldomly be able to get a majority, and parties need to cooperate in order to govern, and this will tend to increase stability. Of course, multiple parties do not guarantee stability, and parties may form blocks that can work like two-party systems.