No, it’s not. Here are the tables produced by the CES:
https://www.bls.gov/ces/tables.htm#ee
Peak-trough tables,
Analytic tables:
UPDATED Table 1. Normal seasonal movements, estimated employment change and test of significance, in thousands
UPDATED Table 2. Detailed industry employment ranked by change and prior 3-month average change, in thousands, seasonally adjusted
NEW Table 3A. Employment changes and tests of significance, seasonally adjusted (in thousands)
UPDATED Table 3B. Employment change compared with recent averages, in thousands, seasonally adjusted
UPDATED Table 4. Employment change from same month a year ago, in thousands, seasonally adjusted
UPDATED Table 5. Estimated change in hours and earnings of all employees, normal seasonal movement and test of significance
UPDATED Table 6. Aggregate weekly hours and payrolls of all employees, in thousands, seasonally adjusted
UPDATED Table 7. Most recent industry-specific peak and trough employment and change through current month, in thousands
Tables A-C2: 90 percent confidence intervals for employment, hours, overtime hours, and earnings (XLSX
Monthly Establishment Data--National
Summary table B. Employment, hours, and earnings, seasonally adjusted
B-1a. Employees on nonfarm payrolls by industry sector and selected industry detail, seasonally adjusted
B-1b. Employees on nonfarm payrolls by industry sector and selected industry detail, not seasonally adjusted
B-2a. Average weekly hours and overtime of all employees on private nonfarm payrolls by industry sector, seasonally adjusted
B-2b. Average weekly hours and overtime of all employees on private nonfarm payrolls by industry sector, not seasonally adjusted
B-3a. Average hourly and weekly earnings of all employees on private nonfarm payrolls by industry sector, seasonally adjusted
B-3b. Average hourly and weekly earnings of all employees on private nonfarm payrolls by industry sector, not seasonally adjusted
B-4a. Indexes of aggregate weekly hours and payrolls for all employees on private nonfarm payrolls by industry sector, seasonally adjusted
B-4b. Indexes of aggregate weekly hours and payrolls for all employees on private nonfarm payrolls by industry sector, not seasonally adjusted
B-5a. Employment of women by industry sector, seasonally adjusted
B-5b. Employment of women by industry sector, not seasonally adjusted
B-6a. Employment of production and nonsupervisory employees by private-industry sector, seasonally adjusted
B-6b. Employment of production and nonsupervisory employees by private-industry sector, not seasonally adjusted
B-7a. Average weekly hours and overtime of production and nonsupervisory employees on private nonfarm payrolls by industry sector, seasonally adjusted
B-7b. Average weekly hours and overtime of production and nonsupervisory employees on private nonfarm payrolls by industry sector, not seasonally adjusted
B-8a. Average hourly and weekly earnings of production and nonsupervisory employees on private nonfarm payrolls by industry sector, seasonally adjusted
B-8b. Average hourly and weekly earnings of production and nonsupervisory employees on private nonfarm payrolls by industry sector, not seasonally adjusted
B-9a. Indexes of aggregate weekly hours and payrolls for production and nonsupervisory employees on private nonfarm payrolls by industry sector, seasonally adjusted
B-9b. Indexes of aggregate weekly hours and payrolls for production and nonsupervisory employees on private nonfarm payrolls by industry sector, not seasonally adjusted
It takes a while to do all that work. And which is it? Do you think the data should come from the IRS or payroll companies? The IRS does not have information on hours or overtime, and the data they do have was collected for a different purpose and would have to be completely reworked by BLS anyway.
As for payroll companies, not every business uses one, and all the data would have to be reworked anyway to consolidate the different formats.
Why does it take months for the QCEW?
https://data.bls.gov/cew/apps/data_views/data_views.htm#tab=Tables
Because it takes a long time to process and analyze and format the data into all the tables in that Link.
You are thinking just of a single number of employed, but that by itself is pretty useless