If illegal immigrants were possible to be identified easily by the IRS, ICE would have taken them over already.
The problem is two-fold. A lot of the immigrants who fall into this "illegal" category are not on the books, they get a brown envelope, and pay little to no taxes at all. And the more "sophisticated" ones look just like your average American. So if you taxed them more, you'd be affecting a lot of the "legal" population as well.
Also, the American economy is full of jobs that no "non-deportable" would like to do. Agricultural jobs come to mind. The current regime's idea of eradicating all illegal immigrants runs contrary to a lot of economic interests (and I read that they've done a lot less deporting on the farms recently. Curious ...) Even if you could just tax them more, you'd still mess with those interests as well.
And while I'm not a tax lawyer, I'm gonna go out in a limb here and say it's not going to be easy to make a tax law like that that isn't going to be heavily scrutinized in the courts because it is unabashedly discriminatory.
I mean by normal people standards, you are correct. He's had to replace a golden spoon up his royal posterior with a silver one. But he still lives in a big house and will never want for money in his life. His involvement did cost him his representative job. He's been royally demoted. So there were consequences for him although I'd be the first to agree they weren't sufficiently punitive.