You’re thinking about computer architecture as designed today. There’s no reason there isn’t a common data structure defined that the CPU can use to select a backup process, much how it uses page table data structures in main memory to resolve TLB misses.
It was slow so operating system devs didn't use it. So it was removed. Probably becouse hardware saved, properly, all registers and software can save only needed few (and sometimes miss something).
In effect: we don't know how secure it was...
But if it was good and Intel removed it then why Intel keeps so many useless crap in ?? Good parts - remove, bad - needed for backward compatibility... Can, finally, someone tell backward compatibility with WHAT ? DOS 4.0 ? Drivers for pre-winonly modems using plain ISA or PCI slots ??
Or maybe just like with EVE Online code (few years ago?) - no one anymore knows how some parts works...