It’s not impossible, it’s just night useless imo.
You will always need help while leveling past 130 as a full support class, maybe even before that. Some mobs will have far to much health and defense even for a priest3 to reliably take down. There’s still a good chunk of weaker enemies later on but you will have to fight bosses and tougher mobs in quests and dungeons.
Then there’s the second issue, you contribute no damage or next to no damage. Parties can only fit 5 players, the more dmg you have the better and safer a dungeon run is. Especially on easier dungeons most parties will simply not want a full support build to tag along. Because it’s a drain on xp for no good reason. (oracles might be the exception with their chance to spawn rare mobs, but that’s just 1 rank)
That also includes the 175 dungeon, which has such easy mobs most classes solo it with ease. Full support classes not so much though, even on my priest3/sadhu my gear would break before i could kill all the enemies. If there’s going to be more “solo friendly” dungeons and people pick up on it leveling a fs will become even more difficult.
tl/dr:
Party slots are limited, fs don’t contribute enough damage to be good options. And leveling/questing is going to be a nightmare.
The closest thing i can think of however is a spirit based cleric with 2priest/1krivis that focuses on monstrance/daino/Zalciai to greatly improve physical dmg for the entire party. What you want aside of that is pretty flexible though.