It isn't on all hardware. Intel has two ME firmwares, a small one for consumer systems, and a big one for corporate/enterprise systems. The small one does not (or at least, should not; is not supposed to) include the remote management features.
In other words, the separation that you describe exists.
Systems with the full firmware sport things such as the vPro branding, and only certain combinations of CPU and chipset support it.
I'd be careful with assumptions on what "consumer hardware" means. There are desktops, NUC units, etc, that shipped with i5 and i7 chips that had vPro.
Even with the CPU, you also need the right chipset and the right firmware to actually light this stuff up. While especially in the laptop sector there are consumer devices that include this, it's far from universal.
In other words, the separation that you describe exists.
Systems with the full firmware sport things such as the vPro branding, and only certain combinations of CPU and chipset support it.