Why can't you do both: (1) count all people and use that for money allocations, while (2) using actual citizenship numbers to allocate congressional representation?
You don't need a law degree to answer this. But since I did spend the three years in law school, let me lay it out:
1. Article 1, Section 2 of the Constitution says "Representatives...shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons."
2. After the Civil War, the 14th Amendment cleaned up the bit about the 3/5ths. Now the rule is that representation is determined based on the “whole number of persons in each state.” It does not say anything about the number of voters, number of adults, number of legal immigrants, number of illegal immigrants. It says "whole number of persons." Put that in your strict constructionist pipe and smoke it!!
3. SCOTUS has previously ruled (9-0 fyi) that you have to do apportionment based upon an actual enumeration of the population. You can't base it on other kinds of statistical techniques (even if valid). Because the freaking Constitution says exactly what is says!!
4. If the Commerce Department is going to do an actual count, then the enumeration clause of the Constitution itself requires the census to be administered in a way that “bear[s] … a reasonable relationship to the accomplishment of an actual enumeration of the population.” Wisconsin v. City of New York (1996; 9-0). Also says that the judgments of the Commerce Secy in administering the Census are subject to judicial review. Very good rule. Because if that were not the rule, there would be nothing to stop a rat bastard hack Commerce Secy from fashioning a questionnaire designed to discourage participation by certain segments of the population.
5. Writing for the Court, Justice Roberts said (and I paraphrase) "get the fork out of my court room you lying rat bastard Wilbur Ross. And please stand by for your indictment on perjury charges for lying in federal court."
6. The reason why Trump CAVED on this issue (in addition to a SCOTUS decision) is that going back to the district court for litigation would mean discovery. And discovery would be BRUTAL. It would just show more and more and more and more rat bastard-ness on the part of the Trumpsters. Thankfully for us all, the lawyers at the DOJ (not Barr but the real worker bee Deep Staters) fragged Barr and Trump badly enough that even Trump/Barr finally had to give up. Which, of course, did not stop them from claiming complete victory! At some point, those damned Deep State lawyers are just not willing to sacrifice their careers, self-respect and law licenses any more in service to a complete clusterfork of bad faith, shameless lies, incompetence and dumb-forkery.
7. Interestingly, SCOTUS has never directly ruled on the question of whether counting illegals in the census (and using their heads for congressional apportionment) is required and legal. So that question is technically open. Alabama is currently suing over that very question. Seems like that case is going to be a loser, but you never know.
8. TL/DR version -- you need a constitutional amendment to apportion on a basis other than actual count of actual people in the country. You may not think it is right or fair to count the illegals, but that is what it says. The 3/5ths wasn't right or fair either -- but we needed an amendment to get rid of that.