While I certainly don't want anyone getting deported because they filled out a census form, encouraging everyone to only answer the first question will cripple decision making for years.
It is illegal for the Census Bureau to act (or let other government agencies act) as a result of what was filled out on a survey/census. Of course, it was hard enough to convince the disenfranchised/minorities/illiterate/homeless/etc. of this in the past when there was not a citizenship question on prior decennial censuses. Add in the irony that those who need federal funding to come to their states the most are the ones least likely to fill it out and thus, reduce the amount their state receives. Anyway...
This question will result in millions and millions of extra taxpayer dollars being spent due to lower response (which, response rates for federal surveys has already suffered a great deal the last two decades). Ignoring the internet option (which will be a reality for most of the 2020 households), it is very cheap (relatively) to send a survey/census in the mail, have it filled out the first time, and placed back in the mail. It is still cheap to send multiple paper surveys/censuses if there no response. It is expensive to hire, train, purchase laptops, and send a person door to door. It is expensive to hire phone operators, train them, and rent a building from which they can operate. These expensive people are hired after there is no luck with the repeated mailings. There will be a lot of non-response.
I like the idea in theory, knowing what our citizenship percentage is in a non-political way, but it shouldn't go on the decennial - at least not until it becomes a normalized question elsewhere (if it ever does) - AND it won't ever be non-political in reality. I say try it out on ACS or CPS, NHES, AHS, CE etc. first or even as a standalone pilot study IF the powers at be feel it is necessary to have this asked. See how awful/well it does and go from there. Also, I think one of the aforementioned surveys would be plenty statistically strong enough to extrapolate/infer for the U.S. population with an acceptable margin of error.
My advice is don't touch the decennial, keep it short and sweet and the response as high as possible while mitigating respondent burden so we can dole out taxpayer money to the states and divvy up the number of seats for the House of Reps as efficiently as possible. There will always be ways to improve what is an "efficient use of taxpayer money" but I don't think adding the citizenship question to the decennial census is one of them.
