I’ve had the same idea before about Prescience as well.
It seems to be able to do everything all Mental Attributes can (excluding will) but with just 1 attribute instead of 3.
Not to mention they can invoke way more banes and boons than Deception, Persuasion, Presence, Learning, Logic, or Perception ever can as you’ve said with Influence.
Great_Moustache already talked about different consequences for different attributes thing.
But the way I’ve personally handled it is this:
Extraordinary can be used to do extraordinary things, but not mundane things.
The rest can be used to do mundane and sometimes extraordinary things, but not often.
In addition, an Extraordinary roll sometimes requires the aid of non-extraordinary attributes.
For example you could use your Prescience to detect and know that supernatural things are at play but you would still need to have good Learning to process the information you gathered and not just get scared and soil your pants.
And Prescience can’t be used to solve a puzzle. That would require the use of Learning. Prescience could give you a hint, but in the end it is up to that character’s natural smarts to solve the puzzle.
Influence I’d say are unable to do the same things Deception, Persuasion, and Presence can.
They’ll either know that you used extraordinary means before or after the fact as Great_Moustache said.
If I were to give examples like with Precognition…
You could use Influence to create the illusion that you are charismatic.
But you would need to either keep using Influence to keep the illusion going which will eventually be discovered, or try to maintain that facade with Deception.
Otherwise, you could just be charismatic and actually have high Presence.
As another example, a trickster with high Deception could trick an Illusionist with just as high Influence as the trickster’s Deception, while an Illusionist trying to trick the trickster might find little success in tricking due to the trickster having enough experience to know something extraordinary must be at play.
Finally, Influence can be used to make temporary friends and then eternal foes, while Persuasion can be used to make eternal foes and convince foes to friendliness or at least neutrality.
Oh, and using Influence to get a better deal instead of Persuasion from a shop might get you arrested regardless of if you succeed or not.