Shadow IT can and does occur. BOFH or no BOFH. But suggesting that the solution to this is simply that IT "become more efficient" (I.E. "do more with less") is beyond farcical. IT isn't some charity, working ourselves to death for the good of our user base and an occasional "attaboy."
If there is more to be done than is currently being done then one of three things is the likely cause:
A) There aren't enough resources available to get all the things done, and IT is prioritising to the best of their abilities, but will never be able to meet everyone's demands.
B) The Manatees "up thataway" are being an impediment to actually expending the resources in place and nothing can get done. (Yet Another TPS Report?!?)
C) The IT staff are all lazy gits who just aren't pulling their weight.
While all of these are possible, I find it difficult to believe that C is probably in most enterprises. If you subscribe to the theory that C must absolutely be true, then I think I have a far more likely scenario for you:
While you consider them to be doing nothing all day, your IT staffs are probably burning themselves out right now trying to meet overwhelming demand. Their health is declining, their sanity is fading and they feel trapped with no way out. (Who has time to look for a new job when there are mortgages/bills/etc. to pay and $deadline is looming?)
When they are finally burnt out and become useless, you probably discard them like spent fuel rods and go shopping for new ones. Why those stupid IT people keep asking for raises, quitting, or getting debilitating stress-induced illnesses is quite simply beyond you.
Sound close to home?
Maybe the IT folks should instead stop working themselves to death and hold out for more money.