The ME "chip" is the Platform Controller Hub. The ME core on that chip is basically your "real" CPU: it initializes your devices into the correct modes at boot, and does things in response to BIOS interrupts, manages DMA regions according to the ACPI DSDT, virtualizes IRQs, refreshes DRAM, etc.

The modern Intel socket CPUs are more like application accelerator cards for this hidden "mother" core. Until recently, you could think of your Intel computer more as an ARC[1] PC with an embedded Intel support slot, than as a pure Intel PC. If you wanted to, you could write a custom BIOS that would boot a Haswell-era motherboard with no CPU inserted, and it would run just fine—because the motherboard already ships with all the CPU it needs to act as a functional computer. (And with the hack on the article, you could run your own software on such a PC, too!)

[1] https://en.m.wikipedia.org/wiki/Synopsys#ARC_International

So no, you can't really remove the ME; it functionally "is" the computer in a lot of ways.

Of course, you could remove its ability to run software other than its kernel—but this doesn't make it "brain dead" or "switch it off"; it just makes it do very slightly less. There's still a lot of (necessary!) stuff going on in there.