All illegal immigrants should be excluded because they are ALL illegal.
Full Stop.
...However, as far as detention and deportation goes, we should focus on the criminals. Then once they all gone, go after folks who have recently entered.
You have made that position plain. But holding that position is dehumanization, no matter how righteous it is. For, as thaiboxerkitten notes above, your "all" includes a non-trivial number of people who were legally within the system, whose status has been retroactively changed to "illegal," and once again, no matter how good you think that action is, and no matter how small you conceive that minority to be, it exists, and counting those people as simple numbers in the "all illegal immigrants should be excluded" group is dehumanization, pure and simple.
You can counter as usual with opinions on how the system ought to work, and how it ought to be reformed, but what is happening now is happening now. The system we have now is the system with which we all must reckon. And whether you think it unworthy of consideration, or permissible collateral damage, actual people are being actually abused by the system right now. People who thought they were operating correctly within the system are faced right now with deportation, which is irreversible and permanent.
With regard to the links above, you say they do not have valid visas, but the second link is exactly about the revocation of student visas which certainly were valid at some time. You're skirting pretty close here to the case of the official asking for papers, tearing them up, and saying "you have no papers!" And before we have to go round and round on this, revoking a visa is NOT THE SAME as saying a person is an illegal immigrant. Even if the revocation is reasonable and valid, and the expulsion justified, the person whose visa is revoked entered the US legally. Conviction of a crime that carries with it the penalty of expulsion is not retroactive.
You know, one of those other constitutional principles we once thought meant something, has to do with ex post facto laws. Now of course we can quibble about just where those lines are drawn, but retroactively declaring legal status illegal is pretty damned shabby no matter if it makes it through the literalist filter.