The thing with FATEs is they serve little to no purpose outside leveling (and even then the XP gain is marginal). Not only that but 'boss' FATEs seem to be mostly a once in a lifetime thing (You will be mine one day, fox lady!). Sure, you may call in friends or your fc to help, but chances are there's almost no one in the zone interested in doing it, or no one [else] in the zone at all.
As much as people hate on RNG, maybe adding RNG based rewards like currencies, reputation, reagents, or even gear would help incentivize doing them, similar to the WT rewards, and rank the rewards in tiers from easiest to hardest so an easy FATE doesn't end up giving something like an i380.