It's unreasonable to quit a game just because you saw 1 person botting. You will see people botting in almost ANY MMO anyway.

Botting is definitely not allowed in FFXIV, and SE always takes appropriate actions against anyone who bots. You need not worry.

I have reported bots many times myself, and after awhile, I never see those names again. So I assume SE has done the work of getting rid of those characters.

However, no companies and no games can eliminate bots entirely. If you can't stand the sight of seeing a single bot, you'll pretty much need to avoid MMO entirely.