This is late, but I think this whole thread is interesting and no one has really answered your question.

I'm a former tenured professor at a major research university who left my position, in part because I came to hate my department (there was an exodus of faculty and it and the university changed substantially), developed a sense that academics is in crisis, and because of family issues (good issues, of the compelling kind).

The salience of grants has increased for a variety of reasons.

The first, and in my mind, most important reason is because of indirect funds on grants, which universities have come to recognize as a revenue stream. It's not just that grants are harder to get, it's that university administration is focused more on profit as a major administrative goal. A former NIH head lamented this once in an article by pointing out that indirect funds (vague, nonitemized pay demanded for things like heat, police pay, etc.) scale linearly with direct funds (the actual cost of the research), even as the actual indirect costs are bounded sublinearly. This is because most universities just negotiate a percentage of the direct funded grant award be indirect funds, but those indirect costs don't continue to increase--e.g., the cost for a heated office and phone line are the same whether you have 100k in direct funds or 1m in direct funds, but the government pays a lot more in the latter case (in which case taxpayer money isn't really paying for the heated office and phone line).

You might recognize this, as do many HN readers, but it's difficult to convey how pernicious an effect it has had. In my time in the department, I saw the attitude change from "people should seek funding to cover their research" to money, and indirect funds in particular, being the primary goal above all else. In preparing grants, by the time I left, grand administrators would strongly encourage you to apply for grants that were maybe 2-4x what were needed for the actual research, just to increase indirect funds that would be paid off the grant. Note that this leads to a spiral, in that inflated asks that are met by the government lead to less money for others.

I do think there's been a shift in administrative goals for whatever reason, maybe due to career administration types increasing, admin coming from outside the university rather than inside, etc. etc. Some of it has to do with changes in how administration is trained for administrative roles per se. Some of it is changes in demands by legislatures, who want to see universities independently turn profits and serve corporate interests more, indirectly or directly. I don't know what it is. But the goals have shifted, and it's enabled by indirect funds from the federal government. The number one thing someone could do to change the grant culture in the US is to eliminate indirect funds, or at least to raise requirements so that they are no longer a source of profit for universities.

Another question is why grant monies are scarcer though. One answer is the pyramid scheme of university research at the moment, which has changed over time. There's a great paper about this by some former federal agency heads (I think in PNAS?) with revealing analyses and figures showing that the indirect fund seeking really picked up steam in the late 90s to around 2000, when per researcher funding was at a peak. Around that time is when universities and researchers started this indirect fund seeking -- admin and researchers realized there was enough to go around, and they could bring in grad students and postdocs ala pyramid scheme to support the indirect funds and it all worked. After that, with increasing newcomers, funding per researcher started to decline, but the incentives for indirect fund seeking remained. So basically in 1999-2000 the current system was established whereby universities get profits from indirect funds from federal agencies, burning through newcomers (grad students and postdocs) to make it work. Although it's not explicitly stated, trainees are essentially seen as disposable labor, justified under some Darwinian idea that the best will rise to the top and the rest will just leave the field. The core issue, whether or not indirect funds are really justified, or whether or not grant money is an appropriate metric of research value, or whether those leaving the field truly have no value in the sense that they should be funded, is left unaddressed.

Another, subtler issue is that many in administration who are former researchers came of age during the pre-2000 era, and so are just used to the system, and don't really see the problems. They were funded early on, and get grant extensions or career funding, and are not faced with the issue of whether or not they would have survived in the current system, so they don't demand any changes (there's a lot of research showing that the average age of first R01 has increased over time, and that older researchers are much more likely to get extensions to large grants than newcomers are to get new research funded). This is exacerbated by the fact that those who did come of age later are used to the current system also, and sort of see it as "well this is what I had to deal with, so you should have to deal with it too."

Another issue that doesn't get as much attention is the decline of tenure. Tenure is a favorite thing to criticize in many circles, but what many don't realize is that it has been severely declining. In many fields or areas of academics, most faculty are untenured, and in other areas tenured faculty have been replaced by adjunct faculty and so forth. The problem with this is that it means that increasingly the faculty that do exist are dependent on grants for survival, which increases the pressure to obtain grants, and more grants. Even if you're tenured, admin sort of sees the untenured grant-contingent faculty and uses them as a comparison (rather than asking how can their time be balanced between teaching and research, or is their research value really best indexed by grant dollars).

There's also a general issue of the black box of increasing university costs, which no one seems to have a good answer to, and is probably due to a combination of things. Increasingly top-heavy admin, "glamor project" funding, increasingly extreme retention salary offers are some of it. Some of it at public institutions is declining state funding, although that doesn't account for private universities. As the pandemic has highlighted, endowments are often fixed in the sense that they're dedicated to specific things, like the library, or whatever.

So:

Increasing university costs no one can really fully explain (or wants to explain).
Decreased state funding.
Decreased federal grant money availability, worsened by inflated grant proposals.
Increased number of researchers due to pyramid scheme incentives.
Increased pressure from admin to seek indirect funds, due to increased profit motive and other factors.
Decreased protections from tenure and other similar things.

Really you could write an entire large book about these issues, and it's only the tip of the iceberg.