> I think it's fine to call 移動動詞 transitive because they take a direct object.
I would agree if it were a direct object. I think mainstream analysis is that を is considered to not always mark the object, but sometimes the place you walk through, and as such frequently stands in opposition to に. I would argue that these are essentially adjunct phrases, not core arguments, although that's always a difficult argument to make in Japanese, since all NPs are theoretically optional, even arguments.
> I can't be bothered to look up what cases actually are and verify this since I find applying western linguistics to Japanese to not be very useful.
As usual, everyone will have their different definitions, but I consider case to be morphological (see also: https://wals.info/chapter/49). I think using vocabulary such as "genitive" muddies the waters. The genitive has a number of functions in, say, Latin or Ancient Greek, not all of which are related to possession. I think it's less confusing to call の a possessive marker - although technically, it's not always possession (e.g. 校長のスズキ先生), so maybe you could even find a better term, like "relational".
> I think mainstream analysis is that を is considered to not always mark the object,
But even in English we can say things like "fly the skies" or "walk the streets", which map reasonably well to how を is used. When it's used for sentences like 自転車を盗んでいるところを捕まった (roughly "caught about to steal a bicycle") however it's harder to understand it that way. It's not the ところ that was caught, but the (implied) topic, probably "I" with no other context
>to not always mark the object, but sometimes the place you walk through
This is anecdotal, but from the 2 Japanese people I've asked they see these usages of を as being the same. Ultimately the way it's classified doesn't really matter so I personally see both ways an being valid.
I would agree if it were a direct object. I think mainstream analysis is that を is considered to not always mark the object, but sometimes the place you walk through, and as such frequently stands in opposition to に. I would argue that these are essentially adjunct phrases, not core arguments, although that's always a difficult argument to make in Japanese, since all NPs are theoretically optional, even arguments.
> I can't be bothered to look up what cases actually are and verify this since I find applying western linguistics to Japanese to not be very useful.
As usual, everyone will have their different definitions, but I consider case to be morphological (see also: https://wals.info/chapter/49). I think using vocabulary such as "genitive" muddies the waters. The genitive has a number of functions in, say, Latin or Ancient Greek, not all of which are related to possession. I think it's less confusing to call の a possessive marker - although technically, it's not always possession (e.g. 校長のスズキ先生), so maybe you could even find a better term, like "relational".