Yes, it is quite ironic. I suppose that the days of not having to prove citizenship harkens back to when there was more of a quasi-national identity, a national culture if you will, in your country. A time when there might have been distinct regional differences, even large in-flows of immigrants, but there was always a national ideal in which to aspire to. There was a commonly accepted notion of what it meant to be American. There was no shame, no compulsion to have to apologize for being American.
In recent years, this has changed. Multiculturalism has taken on a level of acceptance. Once proud ideals are now scorned at and rebuffed. Where it was once intuitive to discern who was American or not, it is now rather complex.
The greatest irony is that most of the same people that quested for the Affordable Care Act are also the ones that will likely voice the greatest opposition over any attempt at standardizing a system for proof of citizenship. The irony intensifies when, in order to implement the revenue collection and compliance measures, the by then larger bureaucratic machine will result in mandating it.
Sadly, the present day is a far cry from when the U.S. was underpinned by the ideal of individualism, of personal responsibility and a common identity.