Why is the prospect of external funding driving hiring?
I agree that there is more pressure nowadays to get funding in areas like pure math in which it's valuable but not mandatory for doing great work.  It's still entirely possible to make an argument along the lines of "Sure, Alice doesn't get much funding, but look how wonderful her papers are," but it's slowly getting harder.

The short answer as to why this is happening is World War II plus inertia.  Here's a longer answer:

The first thing to keep in mind is that grant funding is on average genuinely good for universities, because the overhead rate paid to the university is often higher than any extra costs imposed on the university.  All other things being equal, it makes sense to prefer to hire faculty who can get funding, because they are subsidizing the infrastructure for everyone else (e.g., libraries and internet access).  Of course, all other things are rarely truly equal, and I wouldn't advocate for giving grant funding much weight, but there's a reasonable argument for giving it nonzero weight.

There's also a temptation to use funding as a simple numerical measure of popularity.  Universities should serve the public, and it's clear that people are much more eager to fund work in some topics than others.  It's not crazy to take that into account in university decisions.  However, if taken too far I feel it's an abdication of our responsibility for intellectual leadership.

But why do these things seem to be changing in recent decades?  Universities are generally conservative and slow to change, so it's always worth looking for an explanation of any movement, and in this case I think it's World War II.

Most funding agencies were set up in the aftermath of the war (e.g., the U.S. National Science Foundation dates back to 1950), and the whole tradition of large-scale government funding of research didn't even exist until then.  How academic leaders reacted to it was based on their personal history, and academic inertia meant the changes were slow in coming.  Some of the effects are still surfacing now.

Let's divide things up into academic generations since World War II, giving each generation a twenty year time span to displace the previous one.  Here are my impressions of what happened for cheap or theoretical areas in which funding is not essential to do good work (I'm sure things were very different in big science):


The senior faculty of Generation 1 (1945-1965) were strongly influenced by pre-war traditions.  They had never dreamt of making hiring decisions based on external funding and weren't about to start doing so now.  They were suspicious of how wisely the funding would be allocated, and they saw no reason to think these agencies were even going to continue indefinitely in their present form.
Those in Generation 2 (1965-1985) had still been brought up to be skeptical of paying more attention to funding track records than necessary.  However, they were getting more comfortable with the funding agencies and starting to wonder about how grants could or should be taken into account.  I believe this is the point at which listing grant funding on your CV became mainstream in pure mathematics.
The senior faculty in Generation 3 (1985-2005) went further and began taking funding information into account in ways that would have scandalized Generation 1.  If you didn't list grants on your CV, the dean might now complain about it.  But there was still a sense that this was somehow shallow and historically new.
Generation 4 seems to be taking the trend still further and normalizing it.


Of course this is all vastly oversimplified, and no serious history can be conveyed in a few paragraph-long sketches (even if I were an expert).  However, the key phenomenon is real: the funding landscape was revolutionized after World War II, and academic traditions have slowly been adapting to this fact.