Not 100% true - a microcode-based CPU without microcode isn't able to execute anything, so CPUs will ship with an early version of the microcode that's then (as you say) updated during boot.
They could potentially do that to motherboards, but they could do that anyway (physical access would give you as much access to flash as this vulnerability does). But yes, CPUs should be fine in that respect.
If you can't do that, then this feels significantly less problematic.