Nah, I'd hate XIII even if I never played a single RPG, let alone a single FF game. IX is in my opinion, the only great Final Fantasy game (the rest range from really good to sub par), but I started with VII. I try to let Final Fantasy games stand on their own, since the're made that way and XIII is just a bad game regardless of its predecessors.

I also think the timing of XIII was really unfortunate.

At the time we had the elders scrolls and mass effect games getting all the attention and media praise and thusly we focused on open worlds and choices, features that were secondary or of minor importance in previous FF and turned them into a huge deal.

 On the other hand, while everyone was waiting for the next big RPG, Square took the FF X recipe a little too far and made something that was essentially an action-rpg  blending  (as they said themselves they didn't want to be confined within the rpg genre).

For FF XV I predict Square going the road of XII, instead of X's this time.

I wouldn't go that far, Xenoblade Chronicles was very big scale (in terms of size) and the mainline Pokemon games are massive in terms of profile and sales.  

I was under the impression that XC was highly reminiscent of FF XII.

That's true.  But I've always thought that both of them are how I imagine 3d versions of Secret of Mana