Final Fantasy at it's core is a fantasy game, look at its title and Fantasy is in it. When I think fantasy I think colourful extravagant and flashy skills magic and such with a dark evil to be conquered. So far the flashy skills and magic I enjoy it so far, though the casting animation looks kinda weird. My only issue is the damage text not being over inflated with now what cause the damage being with the visual display. Luckily, at least I think I remember it being there in XIV and know it was in XI, you can turn it on or off. I might turn it off since it looks a little out of place now that it tacks on the action that caused it as long as it wasn't a regular attack.
If your worried about things being too flashy, your into the wrong hobby. Games tend to be flashy for things that we cannot do in reality. Though I'm sure if you want, there will likely be a turn off animations options in the filters somewhere.