The forcing function on my side was to avoid problems when changing jobs. I don't know what problems there might be claiming benefits that you are entitled to, but if you didn't have the change of status registered, that might delay things until you do. If you did change your status but didn't get a card, you can get a replacement one that won't have the text.

One of the things I was concerned for months until I got the new card is the federal government querying the social security database looking for immigrants or discrepancies with any of their other databases and not caring that the discrepancies are of their own making. Being a naturalized citizen with an accent, I keep traveling with my passport for internal trips.