It took me 87 clicks to get a number between 1 and 5. If I managed to have similar RNG throughout all 12, it'd take me 1044 FATEs to complete. Obviously I could have better, or worse, RNG.
Edit:
Set 1
Atma 1 - 87
Atma 2 - 16
Atma 3 - 53
Atma 4 - 13
Atma 5 - 8
Atma 6 - 16
Atma 7 - 3
Atma 8 - 6
Atma 9 - 5
Atma 10 - 9
Atma 11 - 107 (Personally I call this one Western La Noscea *grumbles*)
Atma 12 - 2
This would have been a total of 325 FATEs if we were doing that instead of using a random number generator (which is literally what the system is using). There's no consistency in any of this. All 12 of those could have just as easily been 100+ as 10 or less. I'd personally much rather have a set 'do 50 FATEs' in X zone. Hell, I'd be fine with 75, or 100. At least then I'd KNOW my progress was being counted towards it. I'd KNOW there was a goal in sight instead of 'hoping' that it managed to drop on the next fate after doing that 106th one. I'm sure if you repeat the process enough times you'll eventually have some that end up all being over 100. That's the nature of RNG. Eventually, at some point int the sample you'll have something that's extremely shitty, and something that's really good. Having it set to a specific number per zone seems perfectly reasonable to me instead of leaving those few that DO catch the bad RNG to do the 1200+ FATEs.
Edit 2: Second set took 237. I'll be keeping the number of rolls each individual 'atma' took and continue editing to show total number of rolls per set until I get bored I suppose. It will very likely average out to something reasonable for most sets, but I'm banking on there being some that will be ridiculously low, and others that will be ridiculously high (since that's the nature of RNG). The issue with the system isn't with the people who fall into the lucky - average, it's the few who are getting the shit end of the RNG stick. There is absolutely no reason some should be able to go 200 when others can go 1000+.