It should be as simple as replacing the cartridge to fix the issue at the faucet.
Later, when you have some extra time/money you will definitely want to consider installing shutoffs that work so you can use them in the event that an emergency (broken supply hose, for example) happens, OK?
Finally, the reason no one wants to mess with the marble front is because if it breaks for any reason they'll have to replace it. Simply put, I am sure you couldn't pay a plumber enough money...not unless you would agree to not hold them responsible should the front break....make sense? In other words, this is your issue and the plumber would only be coming in to help...not be responsible for your bathroom marble. They could, of course, cut in an access panel if you asked them...
I would also make note here that all faucets are being made kinda cheaply nowadays (except the really expensive $500.00 faucets) and you can expect to be repairing your faucets every 3-5 years! I know..awaful as it is, it is the way it is and that's that!!
Back to you...