The immigration requirements aren't really a surprise. I don't know of any countries that will just hand out a work visa as long as you have a job offer (special cases like working holidays and transferees excepted - but those tend to be short-term visas).
In the UK, for non-EU working visas (the "skilled labour" scheme) you need to be in a shortage occupation or the company needs to show that they can't recruit within the EU and then if you change jobs within the term of your visa you might just have to do it all over again, depending on whether whoever handles your case at the home office is in a good mood that day or not. NZ & Australia have point systems which are much the same - higher qualifications, high-paying job offer, shortage occupation - preferably more than one of these. At least as an American you wouldn't have to take an English test.
I once had an issue where I couldn't be sponsored for a visa to work in the US, because the visa category in question
required a degree and I was still an undergraduate at the time. Since it was only a summer job, and I was young enough I got in using a third-party sponsor under a working holiday equivalent scheme, the requirements for which were basically a passport and a mildly extortionate "processing fee". If the job had been for more than three months I would have been screwed, though.
Seriously, this is not just a Japan thing. Governments live and die on numbers like immigration and unemployment and if the voters think both of these numbers are too high they'll assume the former is responsible for the latter. So unless there's a genuine shortage in their country of people who can do what you do or you have a large sack of money, they have no motivation to let you in. I can tell you plenty of Stupid Immigration Stories experienced by friends and relatives from around the world - arbitrary requirements, pointless paperwork, rules followed to the letter - and these are for the most part, English speakers immigrating to other parts of the world which are English speaking and it's still a cr☆pshoot. The best part about my naturalisation ceremony was knowing that I would
never have to deal with the UK Home Office again - well, except for the post-naturalisation interview I needed to go through to get my new passport...
"A native English speaker with a job offer to teach and a degree in pretty much anything you like" is honestly a pretty low bar for a work visa. Yes, it's an arbitrary hoop to jump through, but metaphorically speaking the hoop is at a height which is possible to reach and is, at least, not on fire.
tl;dr: all immigration departments, regardless of location, are uniformly horrible pits of bureaucracy. Optimism does not help. Large sacks of money help. If you do not have large sacks of money-- sorry, "qualify for an investor visa", knowing the system well or paying someone to know it well for you also helps. Companies who regularly employ foreign staff will have someone they pay to know the system on your behalf. Companies who do not may not bother hiring foreign staff (unless they already have permanent residency or a transferable visa) because it is just too much hassle.
Also, if you were thinking of doing freelance transcription for US companies while residing in Japan, or otherwise would expect to have income from US sources while you were in Japan, you might want to look into tax laws (or again, pay someone to do this for you). Double taxation could become an issue. Start
here if you really want to read up on taxation rules by yourself.