I don't really understand why nerds have to spec a piece of crud for work always. My all-purpose machine of choice (including telecommutes for staff) are SSD-outfitted Z230's or Optiplex 90x0's. Unlike some piece of crap that's being whipped within an inch of its life while even opening an Excel sheet, it has enough headroom for general OA duties without waiting around. Something goes wrong, on-site (as long as - of course - there isn't a knowitall 'I'm an IT expert' around who tries to fix it and then gets upset when the OEM won't bend to his every misguided whim).
Even for basic duties a half-decent machine will keep on trucking for a long time without issues. And on the flipside, it's more likely that a piece of crap in the first place will give you issues even when doing something basic.
It depends on your telecommuting workflow.
If you sign into the VPN and RDP into a desktop computer or VM at work - your computing experience is 99% reliant on your network connection and the hardware running at the other end of the pipe. Your local machine is a virtually irrelevant near-thin-client.
But, if you sign into the VPN and access work LAN from your local machine (so you're running Office and other applications from the local disk and using your own CPU for CPUing) then the box you're running on locally is much more important.
If you're poor, but you're also lousy at computing and want to make absolutely sure that your weird porno doesn't get saved to a work file server, then speccing out an el-cheapo computer is insurance.