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.)
There's no way to sue for peace with the remaining crowd. They have blood on their hands. They need to be betrayed, isolated and killed. One by one if necessary. The lower grade guys will come forward to give up their superiors if they are relatively clean and they value their lives.
A reign of terror needs an enforcement sanction. I don't believe Saddam and his psycho brood are alive. They are on an autonomic response level now. Where's THEIR bold gambit? Where's THEIR ace in the hole?
You get one sucker punch at Frank Shamrock. That's it. It's not worth it.
They're waiting for Kofi and Jaques to pull some diamond out of their ass.