Well playing alone is entirely your choice, their are plenty of Free Companies out there that you could probably join.
And you already answered you do not mind the story and ff has always been about story so....
Also there are plenty of things to do beside Main story were you can earn experience. Run dungeons, do fates, leves, use food for exp, join a Free Company to help you and also have FC buffs for exp, etc..
This game may however not be for you.