I really don't understand what another heavy armor division is going to achieve at this point. I don't think we are being beaten back by the power of a superior Iraqi battlefield force.
If we wanted to level Baghdad, we could have done that the first night. This is a more subtle and specialized mission.
Maybe some folks are hoping Rommel and his full Panzer Afrika brigade will emerge from the nether-mist and we can line our M-1s up and get into a good ole slobberknocker.
It's a safety thing. And it's worth having on the ground if it does nothing more than prevent a dozen additional combat casualties.
Even without the Fourth Infantry, we could almost certainly take out the RG armor which remains after our bombardment. But if we use twice as many tanks in that battle, we could reduce our losses from, say, two or three tanks, to, say, zero.
Inasmuch as there doesn't seem to be any downside to waiting for the Fourth Infantry, I say we ought to wait.
(The Fourth could also make the eventual thrust against the city of Baghdad proper more quickly and dramatically effective.)