Article argues that Trump misused his platform and appointed some bad candidates at the very least, which is very fair.
And that paragraph was like third from the bottom. Think your own bias is too strong here , the testing angle is the biggest flaw here (since the mask drama is too new) and that's what gets the most attention.
The subtitle of the story identifies three causes (technical flaws, regulatory hurdles, and lapses in leadership) behind a single problem (a lost opportunity to prevent corona-chan's spread in the USA).
The technical flaw being the biggest reason for the problem is kind of a trivial deduction: a new, barely-understood virus requires time to develop a reliable assay to discover it. I mean, duh. There's a reason the article gets that out of the way first and dedicates the least text to it, because it's the only cause with both necessity and sufficiency.
The "regulatory hurdles" aspect is extremely vague in the story, except for the assay detail itself regarding what seems to be a false-positive third probe, and CDC preventing the use of what they believed to be a bad assay. Would simply using the two-probe German assay have been helpful? Seems likely, more test kits is certainly better than less, but how helpful? In all of that, nowhere does the story attempt to actually analyze the odds at play. First known carrier arrived January 15th, went to a hospital the 19th, first CDC test developed the 20th, first carrier confirmed the 21st. Doesn't get much faster than that, yet we clearly know that in those four days before he sought treatment, he had managed to infect others. Considering how no countries anywhere in the world have managed to stop the spread without hardcore quarantine/stay-at-home measures, what the fuck would the testing possibly do beyond maybe flattening the curve for a bit longer? The NYT certainly doesn't know, and didn't even mention any of those dates aside from the first CDC test.
Considering that the majority of the story speaks of characters rather than events or circumstantial realities, it's clear that the overall thrust of the story is just to shit on Trump. The funny thing is that your statement that the story argues Trump "appointed some bad candidates" is actually more your words than the story's own: the story doesn't even make it clear what the particular failings of Azar or Redfield are, though it is sure to make the reader think both of them are absolute incompetents that were too busy fighting each other to get anything done. And that, of course, must be Trump's fault, for not being leaderish enough.