What is missing here so far is maybe what happens on the other side. Some researchers meet for a few days at NSF headquarters to discuss the proposal with some NSF officers. It is called the "panel".

The researchers essentially rank the proposals and decide the outcome:: proposals at the top of the ranking will be funded until money dries out.

Researchers do not know how to evaluate grants the way the NSF wants them to do it. Researchers know how to review papers but not NSF proposals. The broader impacts expectations of the NSF are as obscure to the researchers in the panel as for everyone else. At a panel, after discussing the scientific merits of the proposal, the NSF officers asked the researchers in the panel for broader impacts in the proposal. The first day, the researchers kept pin-pointing (what they thought could be) broader impact items that the NSF officers rejected. As time went by, researchers in the panel started figuring out what kind of broader impacts the NSF officers expected, and could use it to push proposals they liked because of the science. Broader impact sections of the proposals were used to supercharge an already interesting proposal based on the science.

While 15-20 researchers may be in the panel, a few of those will be leading the discussions because of character and interest of looking at these proposals. If these researchers have integrity, the panel will do a decent job. I am sure it is highly dependent on the panel, but the ones I participated in, I thought we did a decent job, maybe with an inclination towards funding young PIs who never got funded before. But networking with NSF officers didn't help any PI; the science dominated the ranking.

Polished broader impact statements appear naturally in tier 1 universities that have many examples and templates of previously funded proposals. Most of it is window dressing; of course there are genuine initiatives but that's not the norm. Asking for diversity statements or whatnot will favor applicants from the alumni and PIs of the Stanfords and Harvards who can network with their peers to gather existing successful statements. After a few generation of sharing these statements, the polishing gets really really good and looks quite serious. It's fairly easy to write broad impact statements with 5 funded examples, much harder when you have none and nobody to talk to (does requiring diversity statements in applications actually hurt diversity candidates? Who knows, studying that question would likely not get funding).

Successful proposals read really well, so well that you wonder how much of the proposed research is already solved. That is a strategy used to write some proposal: when the NSF deadline comes, pick your 1 or 2 most significant unpublished working drafts and write a proposal on the results. Some results you know you already have, others could be interesting generalizations that are within reach, and add to the mix maybe one sexy moonshot. Because you had the paper underway, the story and notation are things you already thought about for a while, and the resulting proposal looks pretty good. If the proposal gets funded, you already have some results to show; good job.

Source: academic who also got CAREER the first time, somewhat burnt out by all these games. Don't get me started on academic awards (the ones with a famous name attached to it)--but let me just say that staying away from those will delay the burnout, a bit; those games are much more rigged than NSF panels.