Before you jump in removing the dvd drive, enter bios setup and check whether it is possible to change boot priority order to select an external flash drive, many old computers don't allow it. I keep all my computers running, both old and very old and modern computers, as long as they switch on and operate. A few of them I still have to use backup software like clonezilla in dvd media because the bios does not allow to boot from a flash drive.
"as they grow older because of the massive amount of malware, spyware, adware, and scareware they accumulate over time" - this is not a reason for technical conscious users who try to have the computer at their peek always. The most probable reason for computer slow-downs is the constant updates and growth in code of windows, plus if you extend of what Apple have done once with iPhones, intentionally slowing down old smartphones, you may also suspect something equivalent may be happening with windows. I have no proof of that, just people complaining about the slow down of windows as years go by, but I have seen a malignant behavior by Microsoft with the old Lumia phones, I have one, and I had to detach the battery as it is being depleted even with the mobile phone switched off. I tried to replace the battery with a new one, with the same result.