It's an important piece of data to know in order to properly enumerate the population and their residency status (ie. Citizen, legal resident, non legal resident)
The constitution doesn't not state that the census is to enumerate legal status. It states that it is done every 10 years to determine how many people live in the U.S. (And the original text, before the 14th Amendment, qualified African Americans as 3/5 of a person).
It's important to understand that this is tied directly to Congressional districting and representation in Congress (as well as how federal dollars are allocated). Last census, the population in Queens supposedly shrank, which we know is nonsense. It's hard enough to get undocumented people to respond -- they don't trust that this information is not being shared with immigration officials. Add a question about citizenship, and you only make it that much less likely to get a true count.
I'm curious what will happen if citizens refuse to answer that question if it is included (which would be my inclination). Will the Census send out workers to attempt to complete the questionnaire? How many times will they come calling?