The largest problem with Rotes is explained in the rules, i.e. from (YS257):
A rote spell is defined as one specific application of evocation in a
single element, such as a fire attack, a particular air maneuver, or a
spirit block. It always manifests in exactly the same way each time,
has the same power level, places the exact same aspect, etc. Any
change in the parameters of the spell disqualifies it from being a
So, how does that help the problem? I'll start out with the first problem of how is he getting a 6 shift rote? Your level is chest-deep from your description, which means that with discipline 5 and conviction 5, he'd still need something to get that extra point.
You see Harry getting hit by that a lot in the books- whatever that extra is (foci and/or aspects)- is a weakness, especially if he's not a well rounded character.
You might say that's a bit heavy handed to use much- and you'd be right. So another way, from that same bit of rules- "It always manifests in exactly the same way each time, has the same power level..." 6 shifts is pretty heavy-duty in terms of damage done. He's pouring a lot of power at every target he hits with that rote. Mortals aren't necessarily able to take that. From disfiguring hits to collateral damage, there's a lot of ways that the consequences of their actions can get them into trouble with mortal authorities and the White Council. They might not be breaking any laws, but bringing that kind of heat down from mortal authorities isn't a good way to make friends.
Last is the fact that if they have optimized their character (and with a 6-shift rote, I'm sure they have), then unless others in the group can pick up the slack and they're just a weapon, there are blind spots. How are the group's defenses against ritual magic? How about against those that are just not affected by the type of magic he's throwing around? Just as Harry runs up against foes where Fuego isn't effective, you can do the same.
One last bit of advice- Fate is by its nature collaborative storytelling, so choose options that advance the story and make the characters' lives interesting, rather than are punitive towards the way that characters are built.