Huh, I'd been under the impression that Alexandrite drops MUCH more rarely from FATEs than Atmas. The way I saw it, the daily quest is the default method for collecting Alex. The devs then realized that folks would be outraged that they'd be forced to spend at a minimum 75 days in order to reach the next stage. In order to appease the ravenous gottagetitnownownow folks, they added HORRENDOUS GRINDS that would allow them to obtain additional Alexandrite, since some people deal better with HORRENDOUS GRINDS than others do. It seemed like a great compromise to me, after the disaster that was the Atma collecting stage.

For my part, I'm satisfied with one Alexandrite per day. I may spend Tomestones on Alexandrite every now and then, and if I happen to get one from a FATE, awesome. But actually farm FATEs for Alex? No. Just no.