In the short term, you're probably right. Most modern desktops and laptops will hopefully last a decade or two (maybe three).
In the medium term, even these will start to break down. One of the key points of failure will be thermal paste; these modern CPUs run quite a bit hotter than a Z80 or 8086 or what have you, and the thermal paste has a finite lifetime (especially the cheaper stuff used in most mass-produced desktops and laptops). Unless you've got a whole bunch of the stuff stocked up, or you're able to setup an immersion cooling rig (with a coolant that's non-conductive and non-corrosive), these PCs will eventually overheat and die. Flash memory and hard drives both have similarly-finite lifetimes, too, so there goes the vast majority of mass-produced storage media (thankfully flash memory longevity is driven by use, so it should be possible to stockpile flash media).
Older chips like the Z80 or 8080/8086 or 6502 tend to avoid the thermal paste problem entirely (by not requiring any sort of heatsink at all), and have simpler memory interfaces (which makes it easier to wire them up to replacement memory, including potentially hand-wound core memory or hand-wired SRAM in a worst-case scenario).
In the long term, even these scavenged Z80s will probably eventually wear out. Hopefully by this time at least some degree of chip fabrication will have been bootstrapped back into existence, in which case replacement Z80s and 8080s/8086s will most likely be possible much sooner than replacement 386s and ARMs.
> x86 PCs and ARM-powered mobile devices are very plentiful, are fairly modular without requiring more sophisticated tools, and avoid a high barrier of entry (i.e. deeper EE experience)
Possibly, from a certain point of view. Apples-to-apples, though, this is very unlikely to be true. Z80-based computers tend to be electrically simpler (by a pretty wide margin) than x86-based or ARM-based computers. There's a lot more supporting circuitry between the CPU and memory/peripherals/etc., which means more components that can fail (and be difficult to replace, especially given the tighter electrical and latency tolerances of the average x86 or ARM motherboard).