Arizona Senator Kyrsten Sinema declared herself a Marxist on Friday. Not Karl. Groucho. As in, "I refuse to join any club that would have me as a member“. She felt compelled to leave the Democrats, she explained, because of the "broken partisan system" and said that she had "joined the growing numbers of Arizonans who reject party politics”.

Declaring herself an Independent might not make a huge difference within the Senate if she continues, as she said she will, voting and behaving the same way on the job. It's too soon to conclude how it will affect her re-election chances in 2024 if she runs, or whatever else she plans to do.

But one thing we know right now: she's wrong about political parties.

Begin with the Senate. Yes, being on a team sometimes means compromising. But Sinema should know that compromises are part of legislating. And parties make legislating a lot easier. Parties allow (more or less) stable coalitions to work together to get things done. Without them, a legislature could devolve into chaos as assorted factions block different proposals.

Indeed, as Sinema should know, the utility of parties in the Senate actually extends into bipartisan deals. Take the immigration Bill she and Republican Senator Thom Tillis of North Carolina are working on with an eye towards getting it adopted before this Congress ends.

When Sinema was operating as a Democrat, Tillis could cut deals on the Republican side knowing that Sinema was able to negotiate in good faith for her party. That could still be the case if Sinema winds up acting as a de facto Democrat. But her ability to speak for Senate Democrats can no longer be assumed.

Party affiliation means that senators occasionally must cast tough votes that might not play well in their home districts in order to advance the party's policy priorities. But in return, senators know they are likely to get the support of the party's senators when they are pursuing the issues they truly care about. Without parties, lawmakers would have to cut deals with their colleagues one at a time, making it hard to accomplish anything.

That's not all! Parties are also very useful for voters. The party label is an incredibly informative shortcut that allows voters to rapidly assess not only what policies a politician is apt to support if elected, but also which groups and interests that politician will be especially attuned to. As with any shortcut, every once in a while voters who depend on it will be misinformed on some details. But overall, it works.

Imagine voting without parties. One would have to carefully research each candidate's policy stances and group loyalties in order to cast an informed ballot. That would be difficult if there were elections for just one or two positions and a handful of candidates for them; it becomes nearly impossible if, as is the case in the US, there are dozens of offices up for grabs in every election cycle.

That's why even when candidates aren't allowed to cite their party affiliation, as is the case in many municipal elections, candidates often find ways of signalling their partisan leanings. And voters like that, because it makes the job of choosing among candidates easier.

Sinema's motives probably have more to do with her precarious position in 2024. But by wrapping her decision in anti-party rhetoric, she is tapping into an old and established strain in US political culture that is, fundamentally, anti-political; it's the same kind of thinking that wishes everyone could just "put politics aside" and get things done. It's suspicious of self-interest, and assumes that there are neutrally good solutions to most policy questions that would be available if only everyone rejected partisan pressures.

And that perspective is common, as far as it goes. Sinema is correct that many people claim to be independents. Few claim to like political parties.

But their behaviour doesn't match those claims. About a third of individuals who say they are independent have attitudes and voting records indistinguishable from people who call themselves Democrats; roughly another third are basically identical to self-identified Republicans. And the remaining third, the true independents, are mostly people less involved in politics.

As political scientist E. E. Schattschneider said long ago: "The political parties created democracy and modern democracy is unthinkable save in terms of the parties." US parties are resilient, and both Republican and Democratic senators will adjust to Sinema's new status. But political parties are at the heart of a healthy democracy, and that will continue to be the case, regardless of Sinema's choices.

• Jonathan Bernstein is a Bloomberg Opinion columnist covering politics and policy. A former professor of political science at the University of Texas at San Antonio and DePauw University, he wrote A Plain Blog About Politics.