Millions of rapid at-home Covid tests are flying off pharmacy shelves across the country, giving Americans an instant, if sometimes imperfect, read on whether they are infected with the coronavirus.

But the results are rarely reported to public health departments, exacerbating the longstanding challenges of maintaining an accurate count of cases at a time when the number of infections is surging because of the Omicron variant.

At the minimum, the widespread availability of at-home tests is wreaking havoc with the accuracy of official positivity rates and case counts. At the other extreme, it is one factor making some public health experts raise a question that once would have been unthinkable: Do counts of coronavirus cases serve a useful purpose, and if not, should they be continued?

“Our entire approach to the pandemic has been case-based surveillance: We have to count every case, and that’s just not accurate anymore,” said Dr. Marcus Plescia, chief medical officer at the Association of State and Territorial Health Officials, a national nonprofit organization representing public health agencies in the United States. “It’s just becoming a time where we’ve got to think about doing things differently.”

There is no comprehensive data on how many rapid tests are used every day, but experts say it is most likely far higher than the number of polymerase chain reaction, or P.C.R., tests, which are completed in a lab and require more time to deliver results, which are reported publicly as aggregate totals.

At least one at-home test company has implemented a system to report results directly to the health authorities. And some local health departments have set up systems for people to report results from rapid at-home tests. But with such a voluntary system, it is possible that millions of tests per day are going unreported, estimates Mara Aspinall, an expert in biomedical diagnostics at Arizona State University who is also on the board of directors of OraSure, which makes rapid Covid tests.

“We certainly don’t want to discourage testing, but at the same time we can’t leave public health authorities blind,” Ms. Aspinall said. “They rely on this information to take proactive and reactive precautions. It’s a very fine balance.”

The quick rise of at-home testing could be a tipping point in a conversation that began for public health experts months ago. At issue is the feasibility of shifting to less frequent case reporting or a “sentinel surveillance” system like the one that public health officials currently use to track other diseases like the flu, which relies on a network of health care centers that track instances of the virus. Overall case numbers are extrapolated based on those case numbers.

Concerns have also emerged about the accuracy of the tests themselves. The Food and Drug Administration said on Tuesday that antigen tests do detect the Omicron variant but not as effectively as they detect other variants.

Throughout the pandemic, daily case counts have played a central role in shaping the policy responses to the pandemic. Cities have instituted mask mandates and closed schools or businesses in response to positivity rates based on daily case counts. In New York City the public school system was shut down at one point when the positivity rate reached 3 percent.

Public health officials, as well as news outlets like The New York Times, continue to use daily case counts to paint an up-to-date picture of the pandemic.

But the case numbers have long been understood as artificially low because of limited access to testing and the prevalence of asymptomatic cases. And compiling those numbers is a labor-intensive task for already strained public health departments.

As a result, many states began shifting away from daily case tallies to reporting fewer times a week over the summer, as cases dropped. Some returned to more frequent reporting as case numbers went back up. But with the Omicron variant fueling a rapid surge in positive cases, states are finding that they can’t keep up. And with so many more cases unreported through at-home tests anyway, there’s little incentive to try.

Dr. Marcelle Layton, chief medical officer at the Council of State and Territorial Epidemiologists, said that her organization had been talking with its members about shifting away from daily case counts, with many that are still doing daily reporting eager to make the shift in the coming months. Her organization has also been in contact with the Centers for Disease Control and Prevention about possible guidance that would direct states to limit daily case reporting. A C.D.C. spokesperson said that the agency did not have plans to change reporting guidance for states.

Tennessee announced last week that it would begin reporting Covid case data weekly, consistent with other infectious diseases. At-home testing and lags in reporting from health care facilities have made the state’s daily case counts inaccurate, the state’s health commissioner, Dr. Lisa Piercey, said at a news conference last week.

“That’s not a sustainable way to do it in perpetuity,” she said. She added: “Daily reporting of numbers is really not that relevant any more. It’s relevant for trends, but the actual number is not that accurate when you don’t know what you don’t know.”

The state will also begin reporting its test positivity rate based solely on P.C.R. tests rather than including the limited number of rapid tests on which it receives reports.

“Everyone knew that this time was coming,” Dr. Layton of the epidemiologists’ council said, adding that the shift was part of a move toward approaching Covid-19 as an endemic disease that the country would have to live with indefinitely, much like influenza.

Other experts say that while daily reporting is not essential in the long term, Omicron’s rapid spread demands that the health authorities maintain daily reporting.

“The reason we got here is because the virus moved so fast — if you’re five days behind, you’re already in the infectious period for many people,” said Stefanie Friedhoff, a professor at Brown University’s School of Public Health. “As long as we’re in this Omicron wave, we need to understand our daily numbers as best as we can.”

Health officials should report case numbers daily, she argued, but should be clearer about the limitations of the data available, she said.

As local public health officials have recognized the limitations of daily case counts, they have turned to a variety of other sources to track the virus’s spread, like hospitalization trends and direct reports from community leaders.

Dr. Jessica Guernsey, health director for the Multnomah County Public Health Department in Oregon, which covers Portland and the surrounding area, said that in light of both at-home testing and the rapid spread of Omicron, those other metrics had become more useful than the emphasis on tracking total numbers of cases.

“With the situation we’re in for with something as aggressive as Omicron, testing, isolation and contact tracing become much less relevant,” Dr. Guernsey said. “At some point, the sort of constant drumbeat of understanding that there’s a lot of Covid out there — it doesn’t help us understand things that much more.”

Nonetheless, the masking of Covid cases by at-home testing has come with some challenges for local health departments, said Dr. Rachel Rubin, senior medical officer for the Cook County Department of Public Health in Illinois. If the positive test results of infected people at schools or nursing homes are not reported, that hinders the county’s ability to advise those institutions on isolation procedures or identify other cases connected to the cluster.

“It’s sort of like a double-edged sword,” Dr. Rubin said. On the one hand, she said, the rise of at-home testing is a positive development, allowing people to isolate when necessary. On the other, it leaves public health officials in the dark. “I think we are only capturing the tip of the iceberg of positive tests,” she said.