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.
High-skilled visas are not connected to an employer and there is no lottery system.beats the hell out of US policies...
I find High Skilled visa to be more useful than a PR. Your parents/Spouse parents can stay with you for longer time ( provided you have a kid less than 7(?) year old)
I just think you were mistaken about the "every other [non-IT] career" part. There is plenty of immigration outside of the discussed trainee program and outside IT, so I just wanted to highlight that. Because otherwise it sounds like Japan has some kind of totally crazy locked down immigration system, but that is really not the case.