If the rule stays, then US citizen children can be left with no adults in their life legally able to raise them in the US. On the other hand, if having a child in the US becomes an automatic ticket to citizenship, there will be a significant increase in children being born for this reason only that may be neglected, and people who want to overstay and are willing to have a child are basically guaranteed the ability to do so.
Another side effect if removed would be that the US border folks may be unwilling to admit pregnant visitors even with very legitimate reasons, because they know there is nothing to stop them from obtaining a green card if desired.
edit to clarify: even without this rule, you have to have entered legally, so just illegally crossing and immediately having a child wouldn't work--you would have to enter as a tourist or otherwise.
But of course if they leave the US willingly (e.g. traveling to their home country) they will be banned from ever coming back.
Yes, they can be deported. This has affected me personally and other members of my extended family.