Unfortunately that's just the way it is. Some people don't want to accept party invites because they're grinding FATES while waiting for the Duty Finder to pop (though if they're a tank it should be nigh instant). I suggest packing a heal spell of your own that you can spam on whoever might need. My first (and main) class is Summoner so I didn't have the problem of being unable to heal or Raise people outside of a party but as I started leveling alt classes I found it frustrating to not have those skills anymore. Summoner honestly has it the best in solo play being able to have a three-man party (yourself, summon, Chocobo) to solo FATES and the like while also doing damage and keeping teammates alive if anyone else shows up.

Auto-grouping would be nice but I can see it easily becoming a problem with leechers being carried through FATES by virtue of standing within the blue area and being counted as part of the party even though they're not doing anything.