There are several motivations for locking down x86. One of the biggest ones was DRM, the protected audio video path. The management engine on Intel also hosts TPM functionality, does some stuff with temperature sensing and fan control, and allows for some remote management. Those are all functions that Intel doesn't want end users or their installed software to be able to tamper with.
The "management engine" is a separate low-power CPU that is able to receive commands when the main power is off. This is used for off-hours patching and provisioning of corporate fleets.
The CPU had previously been an ARC RISC core, but converted to an 80486 a few generations ago.
Yes, all that is true, and AMD has their PSP. ME and PSP represent the "locked-down" part of the x86 platform, running binary blobs that only the CPU makers have the capability to modify (in the absense of exploits.) Not unlike the binary blobs that led Raptor to use an alternative to IBM POWER10.