There are some refurbers that will take office PCs and put a modern-ish GPU, upgrade the PSU etc. That said, Mini PCs don't offer PCIe expansion most of the time, so a GPU upgrade isn't an option. Less appealing compared to new options.
You can get some relatively high end Mini PCs... I mean, around $600 you can get what would be a $2k laptop (minus screen/kb/touchpad). And current gen laptop CPU/iGPU are better than desktop just a few years ago.