Presumably because it would look equally bad and could be legally problematic. Similarly, it is not unusual (for European countries at least, don't know about the US) to stay deportation on humanitarian grounds when a country is unstable or when a person could face abuse or has a medical condition that cannot be appropriately treated there. This means that thousands of people find themselves illegally in Europe (say they have overstayed a visa, been denied asylum, exhausted all possible appeals, etc.) and yet cannot be deported.
There is a kind of hypocrisy in this: Millions of people are stuck in their countries of origin, facing the consequences of war, with no access to proper healthcare, etc. and we don't do much for them but once a person is in our custody, we don't want to dirty our hands by putting them back there. Still, it's a rather well established principle so there is nothing irrational about applying it in this case.
You might try to argue that none of those people are entirely innocent, that without their incarceration they would have lived in these trouble countries anyway, etc. but to most people, especially out of the US, that's not convincing at all and what happens to them is now the US' responsibility. To the extent that the US public image is the main concern, repatriation to an unstable country does not appear to be a win.
The “obvious” solution is to give all those that cannot be convicted of some specific crime in a regular court of law the right to live freely on the US mainland. But since that seems out of the question, there are only ugly options left: indefinite detention without trial, deportation to dangerous places, handing detainees over to suspect regimes, or letting other countries clean up the US' mess.
