> How likely is that the sysadmins were told to 'just make it run cheaper, I don't care' by someone higher in the foodchain?
Having worked in ops for > 10 years, this is how it usually goes.
The SA's job tends to involve a lot of scepticism and caution. You look for problems and try to solve them proactively. One (often easy) way to solve many classes of problems is to throw hardware at them.
Management always pushes back on this tactic. That's reasonable; they need to justify capital expenses (especially if you're self-hosted).
The core issue though is that capital expenses are easy to quantify, while "lost productivity" is much harder to fully account for. If I complain that some hardware upgrade which costs $x could improve productivity, I just don't have hard numbers on my end - it's all napkin math.
In many places reluctance to spend money on infrastructure is also, I think, a symptom of headcount-itis. Managers love to have more employees, and love to have more for them to do, because that makes managers seem more impressive to the org. My manager might have perverse incentives; keeping the SAs busy fighting scaling fires both makes his team look impressive because they're busier, and makes him look better because the capital expenditures are lower.
Obviously, head count is expensive, so this is usually a game of appearances rather than an effective strategy to improve the bottom line. Good insight into productivity is required to catch this kind of stuff, but in the real world I've found that a lot of places just don't have an org structure capable of weighing cost / benefit properly when it comes to infrastructure.