

Totally reasonable question. The question is would you rather have very accurate numbers three months late, or fairly accurate numbers barely a month late? That’s the calculus, and in the current era of a complete lack of trust in government, there’s…kind of an argument for three months late, but really businesses and the public overwhelmingly want the numbers earlier and can adjust based on predictions of revisions (which they do), so one month it is. Plus, these are very old programs and the publishing procedures have been set for quite a long time.
I’d caveat though that there is absolutely no reason you can’t trust these numbers. See my comment above in this thread about reliability of BLS statistics. In an era where there are legions of former public health officials who quit and blow the whistle on things happening in that sector, I’m not sure what makes people think that a bunch of statistics nerds wouldn’t do the same thing. Plus, as the ostensibly pro business side, Republicans like accurate Principal Federal Economic Indicators at least as much as Democrats. Who do you think uses these stats?

Well to your first point, you can go yourself to their website. Everything is public, and they even have a handy page just on revisions: https://www.bls.gov/web/empsit/cesnaicsrev.htm
Secondly, Trump did not fire anyone other than the commissioner, and did not replace anyone at the BLS. They lost a ton due to DOGE and the DRP, but were under a hiring freeze until recently. You can check USA jobs for past listings.
And yes, while leadership could theoretically push certain measurements or methodologies that might skew things in a certain direction, again, at the BLS that functionally can’t be done without a large hue and cry. The commissioner has very little say in program methodologies. Erica Groshen, a former commissioner, is extremely active on social media and often mentions how if there were anything out of the ordinary rank and file would go nuts. You can imagine that’s true given the org has people on both political sides, and gets accused by the other party’s supporters of cooking the books no matter who is in charge, even though methodology changes extremely slowly and is always published online.
To that matter, I am unaware of any changes to inflation measurements during Trump 2, other than I think alternative data sources (e.g. getting datasets from companies/third parties rather than measuring prices at a store), but I’d have to go dig through their methodology publications, which are all wide open and public in the website as well.
The takeaway here is that there is so much sunshine on all of these processes and data it’s functionally impossible for the stats to be a lie. Even earlier reporting this year that imputations (estimating data they can’t physically measure) were way up was still way below the margin of error, and that alone was a huge “scandal”. That was down to the Trump admin starving them of money and staff, and guess what happened a few months later? Suddenly they’re hiring again, because I assume Republicans behind the scenes got pissy about less accurate data, even if it didn’t actually change anything except the measures of accuracy.