I think the problem is with the assumption that 'Influence' is purely a 'social skill'. It includes the use of hard currency. Using Influence can be anything from telling a merchant to "Charge it to this account" to paying with coins (or similar negotiable items- in the Black Library novel Atlas Infernal , the main Inquisitor character buys passage on a local transport with 'Influence' in the form of a handful of small ingots of valuable metal).
And it doesn't preclude having to scrounge for gear- if the Acolytes are in the middle of no-where, Influence doesn't 'conjure' supplies from thin air. There will still be circumstances where PCs need to loot supplies- Influence just negates the driving need to steal stuff to sell for coin a la D&D .
I know what you mean by this, I just dont agree, that cash money is a thing that is portrayed well by influence, as anything you carry with you physically has certain traits:
- it can be stolen or lost
- is DEFINITELY is there, not "maybe, lets see the roll"
- it can be seen by others (subtlety)
- it is much more concrete (its not like you cannot say how much you have)
Even as currently influence covers this aspect, this is odd and not a good way to deal with it.
Easier, maybe, but definitely odd in a lot of situations.