"Choose One Only" Voting, (aka. "Plurality" or "First Past the Post") is universally regarded as the single worst voting system. It works fine if and only if there are two candidates in the race, which is why it is commonly known as the Two Party System.
If there more than two candidates in the race, Choose One Only Voting is extremely vulnerable to a phenomena called The Spoiler Effect. It consistently results in two party domination, and in order to avoid your vote being wasted there are very strong incentives to vote "Lesser Evil" if you aren't sure your favorite can win.
1. The Spoiler Effect:
"Choose One Only" Voting is highly vulnerable to a phenomena called “The Spoiler Effect,” also referred to as “Vote Splitting,” or the “Nader Effect.”
Because of the spoiler effect, "Choose One Only" Voting is wildly inaccurate when there are more than two candidates. Voter blocks who support more than one candidate can end up divided and conquered.
This creates a strong incentive to only vote for the “front-runners.” Voters in a majority can easily lose the election if they don't come together to strategically all vote for one candidate.
Choose One Only Voting gives a huge advantage to candidates who are deemed "viable" and puts voters who have more candidates on their side at a significant disadvantage.
2. Once we solve the spoiler effect, we don't need to have 2 elections:
Primaries generally have lower turnouts and unrepresentative voter demographics. In most cases, primaries bias in favor of older, whiter, and more wealthy voters.
Primary elections are designed to narrow the field, which restricts voter choice in the general election. When people feel like nobody on their ballot represents them voter turnout suffers.
For jurisdictions which use a non-partisan primary and a top-two general election, the spoiler effect can be magnified by the large primary field. When this happens the primary election can actually advance two candidates from the minority faction, guaranteeing an unrepresentative winner in the general.
This two election process makes for a long campaign season, which is disliked by both voters and candidates. Longer campaign seasons advantage candidates with more money, especially those who can afford to take a year or sometimes more off of work while they campaign.
3. Magnifying the influence of Money in Politics
To avoid the Spoiler Effect, voters are coerced into voting for the front-runner on their side who is most “viable.”
The most viable candidate is usually the one who raised the most money and the one with the backing of the media. This gives big money an undue influence over not only voter opinions, but also over voter behavior.
In order to be seen as viable, or "electable," candidates and politicians have to spend a huge amount of their time fundraising. In many cases this leaves them indebted to their donors, breeding corruption.
4. Wasted Votes and Disenfranchised Voters
If you know that your favorite is a shoo-in, or that they don’t stand a chance, then it’s a safe bet that your vote won’t make a difference anyway. Together with the other issues listed above, many people choose not to vote at all because voting their conscience would be a wasted vote anyways.