It always amazes me how fast a particular system can be on linux. I keep a lot of older linux live cds just to see how fast a system can be before determining what OS it will permanently run. If linux had a fast and easy way to remote in like RDP on windows, I probably would have the systems that have more than 4GB of ram on linux. That's the power of a hypervisor if there's enough ram--then I get the best of both worlds.
You bring up a good point about the software. In the beginning, you didn't upgrade hardware for software, it was more or less the other way around--you upgraded hardware just to upgrade so existing software would just run faster. Somewhere along the line (win3.1 enhanced mode?), the push for faster hardware started chasing the software...and it has been ever since. But that's only if the software that has these hardware demands is what you need to get work done. Hence why there's a lot of DOS era machines that run $100k CNC machines and a whole cottage industry surrounding keeping these older machines running--because they do the job.
The 'killer' application today that has runaway hardware requirements is the browser. It has become a memory eating, cpu guzzling, ethernet packet eating slob monster of bloatware. But without it, system requirements and everything else can really be pared down. Just think about xp and not needing to be connected to the Internet--how many requirements and updates and patches and extensions just aren't needed anymore? It's the same with anything if we cut off from the Internet monster. Unfortunately, a lot of 'work' has shifted to the Internet, so there is that aspect. But with security starting to become so dangerous that anything sensitive is pretty much better NOT being connected to the Internet, I think there will actually be room for systems that don't connect to the Internet and have a different upgrade cycle.
For the linux remote access... there's a program that's really good for that, can't remember the name off the top of my head (it's pretty late for me)... or even sure how easy it is to access. Obviously I'm not sure of your technical skills, but at this point, anyone on the forum nowadays is probably pretty well versed in how a computer works.
I know exactly what you mean about browsers! In my opinion, Firefox is the best one for what I do. However I always have htop running to make sure I don't use up all my RAM! This is particularly problematic since I'm an engineering student, and when you are writing a report while referancing multiple documents, life gets a bit hard when you start pushing the 90% mark for RAM XD. I wish there was a better option (there aren't many I found), but I want to stick with Firefox as long as I can since they are realistically the biggest competition to Google Chrome.
Servers often don't need to get upgraded if they have a dedicated use. I've heard of a lab server at my university that ran Debian for 10 years straight without a reboot. It was never upgraded, and it was just some 20 year old PC, but if you're only doing basic things, you can use pretty much any OS going back to Windows 3.x