The reason I don't like this sort of solution is that it doesn't communication to the player (and the GM) what the capabilities of thier characters are.
For example, a scourge of black court vampires has moved into your town and is nom-nom-nomming all the delicious peoples.
Your character:
Knows that attracting their attention is a bad idea, because him and all his friends are going to be nothing bugs on the windshield to them.
Knows that he'll need all the help he can get (and some good tactics to take them on).
Knows that have have to make some serious preparations before he can take them on.
Knows to book "Tomorrow, 9:00 - 9:30 AM, destroy scourge" on his calendar.
The combat system is sufficiently well defined that I have at least some idea of where my character would fall on this spectrum.
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Describing thaumarugy complexity declarations as "whatever" means that I have no real idea if my character can:
Use thaumaturgy to find my lost car keys quicker than just looking for them normally.
Find my lost car keys, at the bottom of the lake.
Find my kidnapped mom with the car keys, because the car used to belong to her.
Call down a Tunguska class even down onto the clan of ghouls that kidnapped and ate my mom.
All of this things might be plot relevant in some way, but without some good guidelines, how can I know what my character can do.
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Consider, at the start of storm front, where everybody sorta assumes that Harry did it, because Harry is one of the few people know around town to have that kind of power.
Notice how that defines a lot of how things go. There are other magical practitioners in town, but killing two people with magic like that is a big enough deal that they probably couldn't have done it, and anyone big enough to have done it would have probably been well known. And that was something like a 30-40 complexity ritual. But what about, say, a 20 complexity ritual? If our characters are investigating that, how does our pool of suspects look? What about a 60 complexity ritual? Does our pool of suspects include people like Harry, Luccio, Morgan, etc? Or is that something only a member of the senior council could do?
But what if the senior council was in session yesterday, with everyone present? Could any of them have put together a complexity 60 ritual between when the meeting ended yesterday and today?
All those questions can't be answered when to rules for how you do thaumaturgy amount to "magic tea party".