Your idea isn't really a fix. It's a regression to an old system and a bandaid at best. It only makes FATEs relevant while the relic is current. After the relic becomes obsolete, then the bandaid is ripped off once again.

Also, have you not been in Eureka at all? Notorious monsters are just FATEs in disguise, usually with more intense mechanics.

So in reality, no one ever stopped doing FATEs in SB, they were just being exclusively completed in specific areas.