Language barrier. I said that. They have their own word for animation, this is only for the english language definitions. In the language itself, they use their own word for animation, foreign words in english are used to denote origin. It's not an excuse for using the word improperly unless you are affected by the language barrier.

The word anime in english has meant that since the start. The usage of the other words as you mentioned were others trying to find new ways to seperate it, which is why anime survived past all of them, as it already meant that in english. Japanime, japanimation denotes ONLY animation from japan, whereas Anime means ALL asiatic animation as stated. Whether it's korea, china, japan, etc.

For example, Red Hawk is anime, but it's not japanime or japanimation. It's korean made and produced. This is why the words japanime and japanimation started falling away after their breif usage. As they weren't accurate to the media that 'fans' attempted to use them for. Which gave rise back the original word that was adopted in english Anime to denote the origin. You'll notice this in the trends of even bestbuy which had also adopted japanimation to define it's area where it kept the media, which then fell away back to anime when it was realized their term was used improperly for the media they had in that section. Which is also why they should probably just seperate it by demographic. Adult animation and all ages animation. As Pokemon, yugioh, X-men evolution, Felix the cat and such are more child fare, but things like spawn, witchblade, Akira, and Fritz the cat are solely adult animation. Notice I didn't say anime, as each title in there has an origin that varies. Fritz the cat for example iirc is Italian made and produced. Whereas something like X-Men evolution was american produced, designed and written, but outsource to japan for animation. The same could be said to Spawn, whereas Witchblade, pokemon, Yugioh and akira are anime.

Back to the language barrier.
All animation in France. No matter where it's made, is Anime. Because anime is their word for animation. That's language barrier. Not the english usages of it.
Though it does create a conundrum for things like Totally Spies, and Martin Mystery which are french produced. Technicly they are anime, since the french word for animation is Anime. It gets more convoluted from there when you learn about the laws for basic airing channels in japan, france and canada. Which is also why the co-production/producing factor also comes into play, which is what helped create these terms to begin with. This is why Nickelodeon can get away with calling Martin Myster anime, even though it's origins are not within asia. It's not false advertising as it's french animation. This is also why they never advertised something like the last airbender as anime, and the most you'll see it stated by actual reporters, news outlets, the channel itself, or its creators as just anime inspired, because it's NOT anime. Its origins are not of asian production for asiatic region intended audiences.

It's not subjective when it comes to english, it's just people making excuses for it. There are plenty of reasons for the way it is, just people tend to ignore the facts for their liberal usage for whatever reason. That doesn't make it the proper usage though. Just their usage, which their usage is subjective, but the proper usage isn't. It is as I stated it is(as per the definitions outlined from the start on the word adoption and usage, not because I said so), and has been since the beginning of the anime boom(late 70s early 80s). Many books (which also traced the word origins back to the early french japan trade agreements pre-disney existence) published on this matter before the urban myths took hold also defined it as such. The massive boom in the 90s though is what gave way to the urban myths taking hold and mis-usage. Everyone was defining it for themselves and to others as they saw it to be right, which wasn't the case for it being 'correctly used' or the correct history talked about. This is why the creator of astroboy is hailed as the god father of anime, even though the word anime, existed before he was even born. He heralded in a new era though of techniques adopted from disney to cut corners on animation, which allowed japan to literally pump out animation in record time.

It became further clouded for what it's not by wizard magazine, EGM, GameFan, etc. These weren't the correct usages but clouded the usage to the mainstream public in english. Notice I keep saying in english. This is because, yes language barriers exist. Every language has their own word for animation on a global encompassing level.

It's like the word tokusatsu, which means a special kind of monster SFX for asian media. Yet there is no such thing as an american tokusatsu, as we would just call it the special effects. It means only that of the effects used in asiatic regions, like Godzilla, Ultraman, sportranger, biokids, and so on. So while yes, The australian Ultraman to japan is tokusatsu, it's just superhero science fiction to everyone else(though since it is ultraman, it's grandfathered into the english definition of tokusatsu). Language barriers. Like they'd call the Adam west batman or even Buffy, tokusatsu, yet in english, it's not. It's like that. Which is why, in english, we use the foreign words, instead of our own word for it. To denote the origin of the work. Just as if we were using whatever language instead of english as the main language, the word animation, would be that language's word for animation.

It also applies to stuff like Kaiju media. Kaiju essentially means rubber suited monsters, or men in suits etc. But it's only used for the asiatic usages of this. There's no such thing as an american Kaiju. There are american monsters like the american godzilla, or Cloverfield, but we just call em giant monsters, etc. They aren't Kaiju. Now granted, shin gojira, (american godzilla) was accepted as being a kaiju in japan thanks to Godzilla Final Wars. But again, that's different(it's grandfathered in since it belongs to the toho Kaiju monster library), and encompasses the language barrier.

Kaiju for example, is just one facet to what makes something Tokusatsu. It's not always prevalent in what japan, nor the english usage of the word tokusatsu needs to have to be tokusatsu.

This also relates to the term super sentai and sentai.
Sentai literally means a task force type media with an intended audience within asiatic regions.
Whereas super sentai is copyrighted by toei for their, well super sentai brand, that gets re-edited into power rangers.
Sportranger for example, is a sentai, but it isn't japan made, and it's not included with the super sentai brand. Same to Biokids which is a filipino made feature. It's a sentai as it's an asian task force intended for an asian audience, but it's not a super sentai as that's a term solely used by toei for the ishinomori initially created brand. Which is why Saban/Disney use Power Rangers for their global term, as Sentai denotes a different demographic and region, but in japan Power Rangers is a sentai. Language Barriers.