Because of the difficulties in using foreign names with Japanese computer systems and paperwork that you mentioned, 通称名 ("nicknames") are essential for many foreign residents. Some groups have been using them for decades now, so even a cursory attempt to get feedback on the new laws would have identified this problem.
Still, some groups of special permanent residents have organized and successfully overturned some of the more odious aspects of the immigration law, like the fingerprinting requirement for alien registration. In particular, the Korean special permanent resident community has some degree of influence on policy because of their size and organization.
Given the general ignorance of the central government (and the immigration bureaucracy as a whole) towards the real needs of foreign residents, I see this decision as ignorance on the importance of 通称名 rather than an attempt to quash the rights of foreign residents. In my experience the local governments tend to be more sympathetic towards the actual needs of foreign residents, perhaps because they have more prolonged interaction with them. (Though as with every government organ in Japan, the interpretation of the law varies wildly depending on which clerk you interact with.)
Troubles like the ones you describe are a large part of why I registered 長瀬ダニエル as a 通称名 and use it for everything I possibly can.