I know people in Tokyo with working visas who are architects, waiters, dish washers, cooks, English teachers, academics, programmers, International school teachers, translators, and business people. All have working (not spousal/relative visas) and none of them have a visa tied to an employer. I have never heard of a visa in Japan tied to an employer (and none of my working visas ever were), with exception of the intra-company transfers.
I also think the path to permanent residency is relatively straight forward for all groups. Stay on a working visa 10+ years with no hiccups or long periods of unemployment, then apply. I have known plenty of non-IT workers to get it.